The DW Math Thread

11112131416

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  • Arctix - Dreamweaver
    Arctix - Dreamweaver Posts: 124 Arc User
    edited April 2013
    Uh, hmm

    I like this proof, but it's a bit circular /O\

    shaddup u r supposed to b perplexed by that problem D<
  • Veneir - Dreamweaver
    Veneir - Dreamweaver Posts: 3,541 Arc User
    edited May 2013
    Needs more maths!
    I'm doing maths reviews today for my final which is tomorrow, so I'll go ahead and throw some of those problems at the thread :3 Of course, that means lots of them won't be in word problem forme, but ah well; I'll fix that for a few if I can think of a way to words them~
    Don't mind my little [trying to be helpful notes]
    Ignore the numbers in (black font) they're there for my reference ahaha 'x3
    Solving for x [insert tilde here aka basic stuffs~]:
    (5) 6 - (6x+4) =18-8x

    (6) x/5 = x/2 - 3 [fractions! LCDs! :3]

    (9) f(-3) = x^2 + 1 [f(#) is f(x) and the number in the (s) is what's plugged in for x :3 Solving in function forms~]

    Domains:
    (10 exe.v.) In the function f(x)=3x - 9, x can equal all real numbers [aka x|x is a real number], and no real numbers are outside of the domain. However, when f(3), the function solves to be 0. Why is this applicable and still inside the domain?

    Solving systems to get an ordered pair of (x,y): [takes two lines to type one problem!]
    2x - 3y = 2
    5x + 5y = 5 (16)
    [No there should not be any 'gross' decimals in that problem x3 No x or y already has a 1 in front of it so tis 'addition method'.]

    Supply models..... sort of. Not really. Yeah it's really not. OTL:
    Decus wants to bring cookies to an event, where the amount of cookies he wants to bring is represented by C=13(b)+105, with b being the amount of burnt cookies per dozen-- for some strange reason, b=3, but we'll just go with that. But Waffles, who only cooks old and burnt cookies, won't allow for this and says the amount of cookies should be C=15(6)+78! (No the ! is not a maths symbol 3:<) How many cookies was Decus originally planning on bringing, and how many were burnt? What fraction of the total amount of cookies does Waffles say have to be burnt?

    "Clearly, the only logical option is Squid." -Decus <コ:彡 <コ:彡
    I'm helplessly needless, and needless to say I owe you | Well I'd pull, teeter away, at the earth with my teeth, to touch your face alive | You lie, helplessly still | As your face falls apart | Well I can make your face brand new | Come take my hand and I'll take your hand | And I will pull you out | Into the sun.
    First fell into an army of noob mobs on 19/3/2009~ Upside-down fox and old-colour squid <┻┻~ [SIGPIC][/SIGPIC]
  • Nariin - Dreamweaver
    Nariin - Dreamweaver Posts: 890 Arc User
    edited May 2013
    Since nobody wants to solve those, I shall.

    ---
    6 - (6x+4) =18-8x
    8x-6x = 18-6+4
    2x = 16
    x = 8

    ---
    x/5 = x/2 - 3
    x/5 - x/2 = -3
    (2x-5x)/10 = -3
    -3x/10 = -3
    3x = 30
    x = 10

    ---
    f(-3) = x^2 + 1 ...I assume just insert the x value?
    f(-3) = (-3)^2 + 1
    f(-3) = 10

    ---
    Uh.. I don't understand the question at f(x)=3x - 9 :o

    ---
    2x - 3y = 2
    5x + 5y = 5
    Well, that clearly is 1 for x and 0 for y

    And the equation stuffies should be um... Inserting one into another perhaps.
    2x = 3y + 2
    5y = 5 - 5x

    2x = 3(5-5x) + 2
    2x = 15 - 15x + 2
    17x = 17
    x = 1

    5y = 5 - 5
    5y = 0
    y = 0

    --
    dozen = 12?

    C = 13(3) + 105 = 144

    C = 15(6) + 78 = 168

    x/12 = 6
    x = 72 ... cookies need to be burned by Waffle's demand... uh... 42,9%?

    Decus was planning to bring 144 cookies, perhaps, 3 were burnt?

    Nop... no idea what I'm talking about or what this task is about :3
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  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2013

    Domains:
    (10 exe.v.) In the function f(x)=3x - 9, x can equal all real numbers [aka x|x is a real number], and no real numbers are outside of the domain. However, when f(3), the function solves to be 0. Why is this applicable and still inside the domain?

    Because 3 is a real number? Am I misunderstanding? Also, I think you're confusing real numbers and rational numbers. Rationals are intuitively said to be "any number that can be expressed as a ratio of two numbers" (EDIT: So long as the denominator isn't zero). Reals are somewhat simpler: "any number that can be a point on a continuous line."

    f(x) is linear and thus (x,y) ∈ R

    Ergo, (3,0) is within the set of all real numbers.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Veneir - Dreamweaver
    Veneir - Dreamweaver Posts: 3,541 Arc User
    edited May 2013
    Because 3 is a real number? Am I misunderstanding? Also, I think you're confusing real numbers and rational numbers. Rationals are intuitively said to be "any number that can be expressed as a ratio of two numbers" (EDIT: So long as the denominator isn't zero). Reals are somewhat simpler: "any number that can be a point on a continuous line."

    f(x) is linear and thus (x,y) ∈ R

    Ergo, (3,0) is within the set of all real numbers.

    Nono you're not misunderstanding my dear; it was more a 'simple explanation' problem than anything, and I suppose it would have had more than one explanations. I sort of thought of when you made the problem with Synta being perplexed at a maths proof/rule.
    What I was thinking of when typing that was that the denominator wasn't 0, so it wasn't something/0, but other logics would work :3 (referring to edits!!)
    Since nobody wants to solve those, I shall.

    I'll go into my maths thing to double check the answers, Nariin [I already did them twice I don't want to do them again ahhh D:] but they all look correct :3

    dozen = 12?

    C = 13(3) + 105 = 144

    C = 15(6) + 78 = 168

    x/12 = 6
    x = 72 ... cookies need to be burned by Waffle's demand... uh... 42,9%?

    Decus was planning to bring 144 cookies, perhaps, 3 were burnt?

    Nop... no idea what I'm talking about or what this task is about :3
    And yeah the supply model attempt problem was pretty much an abomination and for the life of me I couldn't manage to turn it into something that worked how I wanted it to Dyna-style-problem-wise OTL but you did get where I was going with it, yes x3
    "Clearly, the only logical option is Squid." -Decus <コ:彡 <コ:彡
    I'm helplessly needless, and needless to say I owe you | Well I'd pull, teeter away, at the earth with my teeth, to touch your face alive | You lie, helplessly still | As your face falls apart | Well I can make your face brand new | Come take my hand and I'll take your hand | And I will pull you out | Into the sun.
    First fell into an army of noob mobs on 19/3/2009~ Upside-down fox and old-colour squid <┻┻~ [SIGPIC][/SIGPIC]
  • Oliiander - Lost City
    Oliiander - Lost City Posts: 393 Arc User
    edited May 2013
    Olii isn't a fan of maths, nor is she any good with it. So when thrown a particularly difficult question regarding functions and whatnot, it's taking everything I have to not hang myself with a shoelace. If anyone can shed some light on this, it would be much appreciated >:

    f(x+1) = f(x) - f(x-1) + 1
    f(2) = 8
    f(1) = 2

    Calculate: f(2013)

    Functions make my head spin Q.Q

    Also!

    ab = (a/b) + (b/a)

    Calculate: (a+b)(a-b)

    Thank you for your time <:
    My squishiness is (Usually) unrivaled.
    [SIGPIC][/SIGPIC]
    Finally decided to give Olii her own banner.b:chuckle
  • Veneir - Dreamweaver
    Veneir - Dreamweaver Posts: 3,541 Arc User
    edited May 2013
    Bah I can't even check for f(2) = 8 and get 8 right now OTL *just got done cleaning pelt so not really thinky* I tried putting in the 2 for f in three different ways[wut] and got -2, 3, and.... f(2)+1=0, not 8, so I'm really not help right now, I'm so sorry ahhhh.
    Edit: Now four and I still can't get 8 hdfhjfgj. 2/3=/=8 OTL
    *pesters Decusy* D:
    "Clearly, the only logical option is Squid." -Decus <コ:彡 <コ:彡
    I'm helplessly needless, and needless to say I owe you | Well I'd pull, teeter away, at the earth with my teeth, to touch your face alive | You lie, helplessly still | As your face falls apart | Well I can make your face brand new | Come take my hand and I'll take your hand | And I will pull you out | Into the sun.
    First fell into an army of noob mobs on 19/3/2009~ Upside-down fox and old-colour squid <┻┻~ [SIGPIC][/SIGPIC]
  • Oliiander - Lost City
    Oliiander - Lost City Posts: 393 Arc User
    edited May 2013
    Bah I can't even check for f(2) = 8 and get 8 right now OTL *just got done cleaning pelt so not really thinky* I tried putting in the 2 for f in three different ways[wut] and got -2, 3, and.... f(2)+1=0, not 8, so I'm really not help right now, I'm so sorry ahhhh.
    Edit: Now four and I still can't get 8 hdfhjfgj. 2/3=/=8 OTL
    *pesters Decusy* D:

    You can make more sense from it than I can.
    I tackled it again and once more, didn't know how to start. Q.Q
    My squishiness is (Usually) unrivaled.
    [SIGPIC][/SIGPIC]
    Finally decided to give Olii her own banner.b:chuckle
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2013
    Olii isn't a fan of maths, nor is she any good with it. So when thrown a particularly difficult question regarding functions and whatnot, it's taking everything I have to not hang myself with a shoelace. If anyone can shed some light on this, it would be much appreciated >:

    f(x+1) = f(x) - f(x-1) + 1
    f(2) = 8
    f(1) = 2

    Calculate: f(2013)

    Functions make my head spin Q.Q

    Also!

    ab = (a/b) + (b/a)

    Calculate: (a+b)(a-b)

    Thank you for your time <:

    (I'll use asterisks as references, just to make it easier to read.)

    So for the first, it's a recursive sequence:

    f(2) = 8, so...

    f(2+1) = f(2) - f(2-1) + 1 --> f(3) = f(2) - f(1) + 1
    **f(3) = 8 - 2 + 1 = 7

    Keep going until you see some sort of pattern develop...

    f(4) = f(3) - f(2) + 1 = 7 - 8 + 1 = 0
    f(5) = f(4) - f(3) + 1 = 0 - 7 + 1 = -6
    f(6) = f(5) - f(4) + 1 = -6 -0 + 1 = -5
    f(7) = f(6) - f(5) + 1 = -5 - -6 + 1 = 2 (Looks like it may start repeating!)
    f(8) = f(7) - f(6) + 1 = 2 - -5 + 1 = 8 (Hmm... let's keep going to verify)
    f(9) = f(8) - f(7) + 1 = 8 - 2 + 1 (Yep, this is identical to **)


    So really, we have six unique terms: {2, 8, 7, -6, -5, 0}

    Thus, every 6th term is zero. Now, 2012 isn't divisible by 6, but 2010 is; so, f(2011) would be the start of a new repeated set. Ergo, f(2011) = 2, f(2012) = 8, and f(2013) = 7. Another way to do that would be to just divide 2012 by 6, and see that the remainder is one third, meaning that it's [some multiple of 6] + 1/3 (= 2/6). Therefore, 2012 would have been the second term of the new set.



    [Working on the second one but I was asked to post the first.]
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2013
    I tried this problem two different ways, and I couldn't get a nice, neat solution. The one I got is pretty ugly, which tells me I've done something wrong and/or missed something fundamental. As it's now 1:30 am, I think it's best if I return to this at a better time. I can figure it out, I just need some time. I'll leave my current work up in case it helps you out.



    If ab = (a/b) + (b/a), then a = a/b^2 + 1/a --> (a^2 + b^2) / ab^2 and b = b/a^2 + 1/b --> (b^2 + a^2) / ba^2 (Just combining the fractions)

    Now remember that (a + b)(a - b) is just a difference of two squares:

    ***(a + b)(a - b) = a^2 - ab + ba - b^2 = a^2 - b^2

    Based on our above definitions of a and b...

    a = (a^2 + b^2) / ab^2
    a^2 = (a^2 + b^2)^2 / (ab^2)^2

    b = (b^2 + a^2) / ba^2
    b^2 = (b^2 + a^2)^2 / (ba^2)^2 (Same numerator as before since it's the same operation.)

    ****For sake of ease when writing, I'll make (a^2 + b^2)^2 = C. It's getting tedious to re-type it every time ;-;

    So, according to ***, we have...

    a^2 - b^2
    [C / (ab^2)^2] - [C / (ba^2)^2]

    Putting that under one denominator gives us:

    [C*(a^2) - C*(b^2)] / (ab)^4

    Which factors to:

    C[a^2 - b^2] / (ab)^4 --> { (a^2 + b^2)^2 * [a^2 - b^2] } / (ab)^4 (From my shortcut at ****)

    Looking at the numerator from the step above:

    (a^2 + b^2)^2 * [a^2 - b^2] ~~> (a^2 + b^2) * [ (a^2 + b^2)*(a^2 - b^2) ] (Just re-writing it a different way. Look! Another difference of two squares!)

    (a^2 + b^2) * [ (a^2 + b^2)*(a^2 - b^2) ] --> (a^2 + b^2) * [ a^4 - b^4] --> (a^6 -a^2*b^4 + a^4*b^2 - b^6)

    [Work in progress.]
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Arctix - Dreamweaver
    Arctix - Dreamweaver Posts: 124 Arc User
    edited May 2013
    Answer

    I like to fiddle around LHS n RHS alot,so here's my approach {also a2=a squared n b2= b squared }

    ab=a/b +b/a; now (a+b)(a-b)=a2 - b2=[ (a/b)2 - 1 ]b2.......*

    by the equation ab= [ a2 + b2 ]/ab
    -> (ab)2= a2 + b2
    -> a2 + b2 - (ab)2 = 0
    ->a2 + b2(1 - a2) = 0
    -> a2=b2(a2 - 1)
    -> (a/b)2 = a2 - 1,..........**

    replace (a/b)2 value from ** in *

    (a + b)(a - b) = [(a2 - 1) -1] b2 = a2b2 - 2xb2 ( a-squared b-squared - two b-squared )

    its late night for me too n I am sorry if I introduced 0/0 somewhere b:cute
  • Oliiander - Lost City
    Oliiander - Lost City Posts: 393 Arc User
    edited May 2013
    (I'll use asterisks as references, just to make it easier to read.)

    So for the first, it's a recursive sequence:

    f(2) = 8, so...

    f(2+1) = f(2) - f(2-1) + 1 --> f(3) = f(2) - f(1) + 1
    **f(3) = 8 - 2 + 1 = 7

    Keep going until you see some sort of pattern develop...

    f(4) = f(3) - f(2) + 1 = 7 - 8 + 1 = 0
    f(5) = f(4) - f(3) + 1 = 0 - 7 + 1 = -6
    f(6) = f(5) - f(4) + 1 = -6 -0 + 1 = -5
    f(7) = f(6) - f(5) + 1 = -5 - -6 + 1 = 2 (Looks like it may start repeating!)
    f(8) = f(7) - f(6) + 1 = 2 - -5 + 1 = 8 (Hmm... let's keep going to verify)
    f(9) = f(8) - f(7) + 1 = 8 - 2 + 1 (Yep, this is identical to **)


    So really, we have six unique terms: {2, 8, 7, -6, -5, 0}

    Thus, every 6th term is zero. Now, 2012 isn't divisible by 6, but 2010 is; so, f(2011) would be the start of a new repeated set. Ergo, f(2011) = 2, f(2012) = 8, and f(2013) = 7. Another way to do that would be to just divide 2012 by 6, and see that the remainder is one third, meaning that it's [some multiple of 6] + 1/3 (= 2/6). Therefore, 2012 would have been the second term of the new set.



    [Working on the second one but I was asked to post the first.]

    That makes some form of sense! \o/
    Thank you so much!


    I tried this problem two different ways, and I couldn't get a nice, neat solution. The one I got is pretty ugly, which tells me I've done something wrong and/or missed something fundamental. As it's now 1:30 am, I think it's best if I return to this at a better time. I can figure it out, I just need some time. I'll leave my current work up in case it helps you out.



    If ab = (a/b) + (b/a), then a = a/b^2 + 1/a --> (a^2 + b^2) / ab^2 and b = b/a^2 + 1/b --> (b^2 + a^2) / ba^2 (Just combining the fractions)

    Now remember that (a + b)(a - b) is just a difference of two squares:

    ***(a + b)(a - b) = a^2 - ab + ba - b^2 = a^2 - b^2

    Based on our above definitions of a and b...

    a = (a^2 + b^2) / ab^2
    a^2 = (a^2 + b^2)^2 / (ab^2)^2

    b = (b^2 + a^2) / ba^2
    b^2 = (b^2 + a^2)^2 / (ba^2)^2 (Same numerator as before since it's the same operation.)

    ****For sake of ease when writing, I'll make (a^2 + b^2)^2 = C. It's getting tedious to re-type it every time ;-;

    So, according to ***, we have...

    a^2 - b^2
    [C / (ab^2)^2] - [C / (ba^2)^2]

    Putting that under one denominator gives us:

    [C*(a^2) - C*(b^2)] / (ab)^4

    Which factors to:

    C[a^2 - b^2] / (ab)^4 --> { (a^2 + b^2)^2 * [a^2 - b^2] } / (ab)^4 (From my shortcut at ****)

    Looking at the numerator from the step above:

    (a^2 + b^2)^2 * [a^2 - b^2] ~~> (a^2 + b^2) * [ (a^2 + b^2)*(a^2 - b^2) ] (Just re-writing it a different way. Look! Another difference of two squares!)

    (a^2 + b^2) * [ (a^2 + b^2)*(a^2 - b^2) ] --> (a^2 + b^2) * [ a^4 - b^4] --> (a^6 -a^2*b^4 + a^4*b^2 - b^6)

    [Work in progress.]

    Thank you for looking at the question >.<
    This one made a little sense, then the sense took a stroll off the roof after *** >.>
    My squishiness is (Usually) unrivaled.
    [SIGPIC][/SIGPIC]
    Finally decided to give Olii her own banner.b:chuckle
  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited May 2013
    (a + b)(a - b) = [(a2 - 1) -1] b2 = a2b2 - 2xb2 ( a-squared b-squared - two b-squared )

    its late night for me too n I am sorry if I introduced 0/0 somewhere b:cute

    Yea I got that the second time I took a stab at this, but I didn't post it. I still do not think that is the proper solution.
    Thank you for looking at the question >.<
    This one made a little sense, then the sense took a stroll off the roof after *** >.>

    It's awfully convoluted, which means it's wrong. I've still not figured it out. Do you have any idea in what form the final answer would be? As I said before, given that I've not found something succinct and neat, I've either missed something fundamental or there's a problem in my work/the problem.
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
    [SIGPIC][/SIGPIC]
    "Any skills that can be used to kill you will interrupt BB when successful." -truekossy | "...Sage archers are kind of like Mac owners. They are proud of the weirdest and most unnecessary things." -Aesthor | "We ALL know Jesus doesn't play PWI. He may have suffered a lot for humanity, but he'd NEVER punish himself this way." -Abstractive | "I approve of bananas." -SashaGray
  • Oliiander - Lost City
    Oliiander - Lost City Posts: 393 Arc User
    edited May 2013
    It's awfully convoluted, which means it's wrong. I've still not figured it out. Do you have any idea in what form the final answer would be? As I said before, given that I've not found something succinct and neat, I've either missed something fundamental or there's a problem in my work/the problem.

    It was part of a test that I didn't take, so even if there are solutions sent to us, I wouldn't have copy ;~;
    I'm going to blame the question and sweep this one under that carpet. thank you for helping with the first question! f:grin
    My squishiness is (Usually) unrivaled.
    [SIGPIC][/SIGPIC]
    Finally decided to give Olii her own banner.b:chuckle
  • Arctix - Dreamweaver
    Arctix - Dreamweaver Posts: 124 Arc User
    edited May 2013
    Yea I got that the second time I took a stab at this, but I didn't post it. I still do not think that is the proper solution.



    It's awfully convoluted, which means it's wrong. I've still not figured it out. Do you have any idea in what form the final answer would be? As I said before, given that I've not found something succinct and neat, I've either missed something fundamental or there's a problem in my work/the problem.

    Alright one more try with introduction of square roots [ a2 = a squared; r= root ]

    ab = a/b + b/a ;

    -> (ab)2 = a2 + b2 {as before}

    ->a2b2 + 2ab = a2 + b2 + 2ab

    ->a2b2 + 2ab = (a + b)2

    -> r[a2b2 + 2ab] = a+b ......*

    -> r[a2b2 - 2ab] = a-b ........**do as above with - 2ab

    now (a+b)(a-b) = r[ (a2b2 + 2ab)(a2b2 - 2ab) ]

    I dont think so I've done a miscalculation here
  • Superfeng - Lost City
    Superfeng - Lost City Posts: 125 Arc User
    edited May 2013
    You have ab = a/b + b/a

    This becomes (a^2)(b^2) = a^2 + b^2 as everyone else has observed.

    Now, (a^2)(b^2) - a^2 - b^2 = 0

    --> (a^2)[(b^2) - 1] - b^2 + 1 = 1

    --> (a^2)[(b^2) - 1] - [(b^2) - 1] = 1

    --> [(a^2) - 1][(b^2) - 1] = 1

    So either, (a^2) - 1 = 1, (b^2) - 1 = 1

    or (a^2) - 1 = -1, (b^2) - 1 = -1

    If the latter case were true, then it'd imply a^2 = 0, so a = 0, and similarly b = 0.
    But in your original problem, you are dividing by a and b, which means a and b cannot be 0.

    Now the first case would imply that (a^2) = 2, (b^2) = 2

    You are looking for (a+b)(a-b) = a^2 - b^2 = 2 - 2 = 0.

    So yeah the answer is 0.
    Superfeng - Level 101 Lost City Blademaster, retired.
  • Superfeng - Lost City
    Superfeng - Lost City Posts: 125 Arc User
    edited May 2013
    Give me some real math problems please.

    No one wants to do math anymore. Where are Fizban, Cheze, and Yorkin? :(

    More 5th year grade math:
    Superfeng - Level 101 Lost City Blademaster, retired.
  • Fissile - Archosaur
    Fissile - Archosaur Posts: 607 Arc User
    edited May 2013
    You have ab = a/b + b/a

    This becomes (a^2)(b^2) = a^2 + b^2 as everyone else has observed.

    Now, (a^2)(b^2) - a^2 - b^2 = 0

    --> (a^2)[(b^2) - 1] - b^2 + 1 = 1

    --> (a^2)[(b^2) - 1] - [(b^2) - 1] = 1

    --> [(a^2) - 1][(b^2) - 1] = 1

    So either, (a^2) - 1 = 1, (b^2) - 1 = 1

    or (a^2) - 1 = -1, (b^2) - 1 = -1

    If the latter case were true, then it'd imply a^2 = 0, so a = 0, and similarly b = 0.
    But in your original problem, you are dividing by a and b, which means a and b cannot be 0.

    Now the first case would imply that (a^2) = 2, (b^2) = 2

    You are looking for (a+b)(a-b) = a^2 - b^2 = 2 - 2 = 0.

    So yeah the answer is 0.

    Lol what?

    let x = a*a - 1 and y = b*b - 1

    You are saying if xy = 1, then x or y must be 1 or -1 and that just makes no sense.

    If you factor it to (a+1)(a-1)(b+1)(b-1)=1 you can get forms for a and b like a = 1/[(a-1)(b+1)(b-1)] - 1, then plug those into (a+b)(a-b) and see what you get. I'm guessing the answer is not 0.
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  • Superfeng - Lost City
    Superfeng - Lost City Posts: 125 Arc User
    edited May 2013
    I might have umm, assumed a and b were integers b:surrender
    Superfeng - Level 101 Lost City Blademaster, retired.
  • HrunsPanda - Archosaur
    HrunsPanda - Archosaur Posts: 1,136 Arc User
    edited May 2013
    Is this the "help with my homework" thread ? b:laugh
  • darknessofmy
    darknessofmy Posts: 164 Arc User
    edited August 2013
    6+3+6+3+6+3+6=6666666
  • BloodyOne - Dreamweaver
    BloodyOne - Dreamweaver Posts: 88 Arc User
    edited August 2013
    I Cant beleive this thread is still going on lol
    b:shocked no signature
  • ColdAsLife - Dreamweaver
    ColdAsLife - Dreamweaver Posts: 432 Arc User
    edited October 2013
    I Cant beleive this thread is still going on lol


    I hear you, man, but I'm happy about it. Decus deserves even better! b:thanks
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  • Decus - Dreamweaver
    Decus - Dreamweaver Posts: 5,033 Arc User
    edited November 2013
    I hear you, man, but I'm happy about it. Decus deserves even better! b:thanks

    It's nice to see you still around. You're very kind. Thank you, Grim.


    As for this thread, I've not actually received any questions lately. Alongside that, I've been focusing on some more technical things as of late and so math sort of falls to the wayside :(
    Proving that not only archers do math since 2009. b:victory
    Current math challenge: pwi-forum.perfectworld.com/showthread.php?t=1029711&page=45
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  • opkossy
    opkossy Posts: 11,177 Community Moderator
    edited January 2014
    PS. You can un-sticky it since I don't plan to really keep track of it and no one asked anything for a long time.


    DW doesn't get any more math sticky. b:cry

    Necro period begins as of this post.
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  • Veneir - Dreamweaver
    Veneir - Dreamweaver Posts: 3,541 Arc User
    edited January 2014
    OPKossy wrote: »
    DW doesn't get any more math sticky. b:cry

    Necro period begins as of this post.

    *sniffles* My maths class was starting up in a few days since classes next week, too >:
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  • opkossy
    opkossy Posts: 11,177 Community Moderator
    edited January 2014
    We must stalk Decus. For maths... for honor.... FOR POST COUNTS!
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  • ovenusarmanio
    ovenusarmanio Posts: 6,695 Community Moderator
    edited January 2014
    Nuuu *tries to put the duct tape back on the thread but it isn't sticky anymore* b:cry

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  • torquoisegamer
    torquoisegamer Posts: 96 Arc User
    edited November 2014
    a lot? you should've gave me a map =[
    is this a map? http://www.ducksters.com/geography/south_america_map_coloring.jpg

    EDIT:! oh I THINK THE ANSWER IS 4! IDK :D here's my map: http://i.imgur.com/vn0kgJ3.png
    ps i didn't know that south america had like 10 countries

    it's like that thread on dyna forums with the math clock... and how the 7 on clock was 6.9 and the nine had the line thingy on it.... OTL he will never understand!

    Four is correct, since Decus doesn't seem to have responded. Four color theorem states that on any flat surface (and since South America doesn't have any fragmented countries such as Russia, South America can be treated as a flat surface), a maximum of four colors is needed to fill each area with a country so that no two countries are touching each other.
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  • SweetieBot - Lothranis
    SweetieBot - Lothranis Posts: 18,978 Arc User
    edited November 2014

    Four is correct, since Decus doesn't seem to have responded. Four color theorem states that on any flat surface (and since South America doesn't have any fragmented countries such as Russia, South America can be treated as a flat surface), a maximum of four colors is needed to fill each area with a country so that no two countries are touching each other.
    This looks like a NECRO!

    torquoisegamer replied to a message that was 10 months 19 days 34 minutes old.

    Any thread over one month (30 days) old is considered to be a dead thread and you're not supposed to post in them. The person you are replying to probably doesn't care any more or can no longer be found on the forums. The topic itself could be out of date. Next time just make a new thread.

    Let's see how long it takes for a mod to close this :)
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