Question

Encircle the error in the following "proof" that the two arbitrary numbers are equal to each other. Let a and b the arbitrary numbers such that a is not equal to b. Then,
(a - b)^2 = a^2 - 2ab + b^2 = b^2 - 2ab + a^2
(a - b)^2 = (b - a)^2
a - b = b - a
2a = 2b
a = b

Answer 1

There is a + and a - root of each squared term.

Just because (-4)^2 = 4^2 does not mean -4 = 4.

Answer 2

Hi Steve! So with your explanation, am I correct in saying that the error in the above given is (a - b)^2 = (b - a)^2?

Answer 3

no, it's the next line. The squares <b>are</b> equal; it's the assumption that the roots are equal which is wrong.