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-   -   The final question on my alg2 exam last year. (http://www.flashflashrevolution.com/vbz/showthread.php?t=50468)

RainGame53 09-24-2006 11:35 AM

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.

Benny1 09-24-2006 11:39 AM

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 09-24-2006 06:41 PM

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 09-25-2006 09:03 AM

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

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 09-25-2006 09:09 AM

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 10-28-2006 08:56 PM

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 10-28-2006 09:37 PM

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

lord_carbo 10-28-2006 10:08 PM

Re: The final question on my alg2 exam last year.
 
1/4 = inf

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

spyke252 10-28-2006 11:06 PM

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

Originally Posted by chickendude (Post 966077)

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 10-29-2006 11:55 AM

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 10-29-2006 12:44 PM

Re: The final question on my alg2 exam last year.
 
Kids in a pre-algebra class could understand that much.

studmuffin51306 10-29-2006 03:50 PM

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

Originally Posted by vashthestampede0987 (Post 967045)
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 10-29-2006 03:59 PM

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

Originally Posted by studmuffin51306 (Post 967193)
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- 10-29-2006 04:21 PM

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

Discuss.

Afrobean 10-29-2006 04:30 PM

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.

spyke252 10-29-2006 04:37 PM

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.

Afrobean 10-29-2006 04:53 PM

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.

Kit- 10-29-2006 08:40 PM

Re: The final question on my alg2 exam last year.
 
Actually, square roots are by definition positive. But you're getting close.

Afrobean 10-29-2006 08:45 PM

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

Originally Posted by Kit- (Post 967552)
Actually, square roots are by definition positive. But you're getting close.

rofl

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.

Kit- 10-29-2006 08:48 PM

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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