Question

If x/y+y/x=-1 (x is not equal to y,x is not equal to 0,y is not equal to 0 ) what will be value of x^3-y^3

Answer 1

We know that,
x³-y³=(x-y)(x²+xy+y²)........................1
Given that,
x/y+y/x=-1

(x²+y²)/xy=-1

x²+y²=-xy

x²+y²+xy=0

(x²+xy+y²)=0
Multyplying by (x-y) on both sides we get,
(x-y)(x²+xy+y²)=(x-y)×0
By eq1 we get,
x³-y³=0

Hence x³-y³=0.