if` x/y + y/x = -1 ( x, y != 0 )` , then the value of `x^3 -y^3` is

Options

A. 1
B. `-1`
C. 0
D. `(1)/(2)`

Answer

C

Explanation

Given , `" " (x)/(y)+(y)/(x)=-1`
` implies (x^(2)+y^(2))/(xy)=-1`
`implies x^(2)+y^(2)=-xy`
`implies x^(2)+y^(2)+xy=0 " " …(i) `
Now ` x^(3)-y^(3)=(x-y)(x^(2)+xy=y^(2))`
`" " ["using identity ", a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2))]`
`=(x-y)xx0=0 " "["from Eq.(i)"] `