This is wrong, but I don't remember why.

Factual Questions
1

This is wrong, but I’m not sure where the logic fault lies. Can someone more mathematically inclined point it out?

Given: a = b

 Then: ab = a^2

         ab - b^2 = a^2 - b^2

         b(a - b) = (a + b)(a - b)

         b = a + b

         b = 2b

         1 = 2
2

Since you start with the assumption that a = b, you have that a-b = 0. When you divide both sides by a-b you are dividing by zero, which is a no-no.

Looked at another way, before you divide by a-b the two sides are equal because each side is something multiplued by zero, which is itself zero, so both sides are equal regardless of what the something is (unless the something is infinity, but it isn’t in your example). 1 X 0 = 2 X 0, so there’s no contradiction

3

Alright, let’s just substitute “2” in for all the unknowns

Given: a = b–>2=2
Then: ab = a^2 —> 4=4
ab - b^2 = a^2 - b^2 —> 2(2)-4=4-4–>0
b(a - b) = (a + b)(a - b) —>2(2-2)=(2+2(2-2)
2(0)=(4)(0)
0=0
b = a + b ----> 2=4----> Unless things have changed since I took Algebra I, 2 does not equal 4
b = 2b —> 2=4—> 2 still does not equal 4
1 = 2—> No more than 2 equals***

****disclaimer: I’m NOT a math person, and I probably screwed this up horribly. Please do not laugh at me too much.

4

Sneaky, sticking that division by zero in there. Everything looks correct, so you tend to not plug in real numbers… which is, of course, what would lead you to realize what they were having you do.

Thanks!

5

well, that was exciting.
I’ve been out of school since 1972. I wasn’t a math major, but I did tutor a whole lot of folks in algebra etc. back then (my buddy Paul owes me BIG time for passing algebra).

And, I figured it out, too…

I’ll have to thank my math teacher.