Question

if x/y + y/x = -1 then the value of x³-y³ is​

Answer 1

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x³ - y³ = (x-y)(x²+xy+y²)..............(i)

Given that,

x/y + y/x = -1

(x²+y²)/xy = -1

x² + y² = - xy

x² + y² + xy = 0

(x²+xy+y²) = 0

Multiply by (x-y) on Both sides

We get,

( x-y )( x²+xy+y² ) = ( x-y )×0

By Equation 1 , We Get,

x³ - y³ = 0