a/b + b/a = x

Question

a/b - b/a = y

in the equation above, if a is (not equal) to 0 and b is (not equal) to 0, which of the following must be equal to x^2-y^2?
a. 2
b. 4
c. ab/2
d. a^2 b^2/2
e. 4a^2b^2

Answer 1

x^2 - y^2 = (x+y)(x-y)

but x+y = a/b + b/a + a/b - b/a = 2a/b
and x-y = a/b + b/a - a/b + b/a = 2b/a

so (x+y)(x-y) = (2a/b)(2b/a) = 4