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#1 |
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FFR Player
Join Date: May 2005
Posts: 61
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1. Let a and b be equal non-zero quantities
a = b 2. Multiply through by a a^2 = ab 3. Subtract b^2 a^2 − b^2 = ab − b^2 4. Factor both sides (a − b)(a + b) = b(a − b) 5. Divide out (a − b) a + b = b 6. Observing that a = b b + b = b 7. Combine like terms on the left 2b = b 8. Divide by b 2 = 1 We had to write what causes the false answer and why. What a weird problem. Last edited by RainGame53; 10-29-2006 at 01:47 PM.. Reason: lol it was a typo, sry for confusing the **** outta all of you |
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#2 |
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FFR Player
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wow, that's retarded, it's so obvious that a=b, so therefore when they divide by (a-b) they're dividing by zero...
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#3 |
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FFR Player
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Here's why it's false
When you factor 2a-2b = ab-2b, it should be: 2(a-b) = b(a-2) If I'm correct, that would be as far as you could factor without further information (a-b)(a+b) is the difference of squares, which equals a^2 - b^2 Last edited by masterhickle; 09-24-2006 at 06:45 PM.. |
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#4 | |
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FFR Player
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Quote:
So following through: a^2 - 2b = ab-2b a^2 - 2b = b(b-2) b^2 - 2b = b(b-2) b(b-2) = b(b-2) 1 = 1 That whole question is enormously retarded. Anyone with any knowledge in math could tell that the whole thing is done wrong. Last edited by Tokzic; 09-25-2006 at 09:11 AM.. |
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#5 |
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FFR Simfile Author
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This is the oldest question ever.
But, yeah, it's false because a-b = 0, can't divide by 0.
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Patashu makes Chiptunes in Famitracker: http://soundcloud.com/patashu/8bit-progressive-metal-fading-world http://img.photobucket.com/albums/v216/Mechadragon/smallpackbanner.png Best non-AAAs: ERx8 v2 (14-1-0-4), Hajnal (3-0-0-0), RunnyMorning (8-0-0-4), Xeno-Flow (1-0-0-3), Blue Rose (35-2-0-20), Ketsarku (14-0-0-0), Silence (1-0-0-0), Lolo (14-1-0-1) http://i231.photobucket.com/albums/ee301/xiaoven/solorulzsig.png |
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#6 |
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Falcon Paaaauuuunch!!!!!!
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When it said multiply through by a, I thought it was just a type-o, and that it meant multiply by 2, since that's what was required to get 2a, and I didn't even notice at first that the ab didn't have a 2. The factoring was totally wrong, since the 2s just disappeared. Even with the 2s just disappearing, it would not factor into (a+b)(a-b), so that's totally wrong. After the b got factored out of the other side, there wouldn't be a b left in the last term, so it's even more wrong. a-b=0 may be true, but I'm not sure that's really wrong, it just makes you lose zero as a solution of the equation if it were one, but it's otherwise okay, I thought.
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#7 |
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Away from Computer
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#9 |
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FFR Player
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yeah, you cant assume the derivative of a summation is = to the summation of its derivative.
x ∑x = x(x) + x(x-1) + x(x-2) + ... + x = x(x + x-1 + x-2 + ... + 0) 1 =x(x+2x+3x...+x(x-3) + x(x-2) +x(x-1)) =x(x(1)) =x^2 And I really didn't do anything. |
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#10 |
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Away from Computer
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yeah, since x has to be an integer, the left side isn't continuous or differentiable
it's a simple trick
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#11 |
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FFR Player
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Kids in a pre-algebra class could understand that much.
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#12 | |
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FFR Player
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Quote:
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#13 |
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FFR Player
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Well, you aren't in preAlgebra anymore, are you?
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#14 |
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Private College
Join Date: Feb 2006
Location: Lol badger
Posts: 536
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![]() Discuss.
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#15 |
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Admiral in the Red Army
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2i^2 isn't the same as (2i)^2
I assume that's what you're saying, because otherwise, that 4=2 comes out of nowhere.
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#16 |
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FFR Player
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Hm...
There aren't any visible problems with that proof. However, the 4=2 is unnecessary, as if -1=1, then any number is equal to any other number. But I assumed you added 3 to both sides to get the 2=1 answer. |
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#17 |
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Admiral in the Red Army
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Oh I see the problem now.
Because of the square root, it's really plus or minus. It's sort of like saying this: ±1 = ±1 1 = -1 Which is obviously wrong.
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#18 |
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Private College
Join Date: Feb 2006
Location: Lol badger
Posts: 536
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Actually, square roots are by definition positive. But you're getting close.
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#19 | |
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Admiral in the Red Army
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Quote:
So I guess -1 squared isn't 1. You might simplify things by saying that square roots are always the absolute value, but that's not entirely mathematically correct.
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#20 |
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Private College
Join Date: Feb 2006
Location: Lol badger
Posts: 536
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Solutions to x^2-a=0 are not by definition positive.
Solutions to x=a^(1/2) are by definition positive.
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