The final question on my alg2 exam last year.

[RainGame53]

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.

[Benny1]

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...

[masterhickle]

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

[Tokzic]

Re: The final question on my alg2 exam last year.

2. Multiply through by a

2a = ab

Wrong. a*a is a^2, not 2a. Actually, more steps are done wrong than right in that question, but that's the first mistake, so all others are irrelevant.

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.

[Patashu]

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.

[Doug31]

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.

[chickendude]

Re: The final question on my alg2 exam last year.

[lord_carbo]

Re: The final question on my alg2 exam last year.

1/4 = inf

Also, stupid thread, mathematical fallacy, etc.. Nothing to discuss.

[spyke252]

Re: The final question on my alg2 exam last year.

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.

[chickendude]

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

[vashthestampede0987]

Re: The final question on my alg2 exam last year.

Kids in a pre-algebra class could understand that much.

[studmuffin51306]

Re: The final question on my alg2 exam last year.

Kids in a pre-algebra class could understand that much.

I am in Algebra II and I have no idea what y'all are talking about

[spyke252]

Re: The final question on my alg2 exam last year.

I am in Algebra II and I have no idea what y'all are talking about

Well, you aren't in preAlgebra anymore, are you?

[Kit-]

Re: The final question on my alg2 exam last year.


Discuss.

[Afrobean]

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.