a/b + b/a = x

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

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

so whts the answer

To find the value of x^2-y^2 in terms of a and b, we can first solve the given equations:

1. a/b + b/a = x
Multiplying both sides by ab gives us:
a^2 + b^2 = axb

2. a/b - b/a = y
Multiplying both sides by ab gives us:
a^2 - b^2 = ayb

Now, let's simplify:

(x^2-y^2) = (a^2 + b^2)^2 - (a^2 - b^2)^2
Using the difference of squares identity, we have:
(x^2-y^2) = [(a^2 + b^2) + (a^2 - b^2)][(a^2 + b^2) - (a^2 - b^2)]
(x^2-y^2) = [2(a^2)] x [2b^2]
(x^2-y^2) = 4a^2b^2

Therefore, the value of x^2-y^2 is equal to 4a^2b^2.

Out of the given options, the correct answer is (e) 4a^2b^2.