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The final question on my alg2 exam last year.
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. |
Re: The final question on my alg2 exam last year.
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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Re: The final question on my alg2 exam last year.
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 |
Re: The final question on my alg2 exam last year.
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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. |
Re: The final question on my alg2 exam last year.
This is the oldest question ever.
But, yeah, it's false because a-b = 0, can't divide by 0. |
Re: The final question on my alg2 exam last year.
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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Re: The final question on my alg2 exam last year.
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Re: The final question on my alg2 exam last year.
1/4 = inf
Also, stupid thread, mathematical fallacy, etc.. Nothing to discuss. |
Re: The final question on my alg2 exam last year.
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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. |
Re: The final question on my alg2 exam last year.
yeah, since x has to be an integer, the left side isn't continuous or differentiable
it's a simple trick |
Re: The final question on my alg2 exam last year.
Kids in a pre-algebra class could understand that much.
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Re: The final question on my alg2 exam last year.
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. |
Re: The final question on my alg2 exam last year.
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. |
Re: The final question on my alg2 exam last year.
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. |
Re: The final question on my alg2 exam last year.
Actually, square roots are by definition positive. But you're getting close.
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Re: The final question on my alg2 exam last year.
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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. |
Re: The final question on my alg2 exam last year.
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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