Question

if x/y + y/x = -1 , then the value of x^3 - y^3 is ???​

Answer 1

Answer:

$\displaystyle \sf \longrightarrow x^3 - y^3=0$

Step-by-step explanation:

Given :

$\displaystyle \sf \dfrac{x}{y} + \dfrac{y}{x} =-1$

Solving it further we get :

$\displaystyle \sf \dfrac{x^2+y^2}{xy} =-1$

$\displaystyle \sf x^2+y^2 =- xy$

$\displaystyle \sf x^2+y^2 + xy =0 \ ...(i)$

We know :

$\displaystyle \sf a^3 - b^3=(a-b)(a^2+b^2+ab)$

Using ( i ) we get :

$\displaystyle \sf \longrightarrow x^3 - y^3=(x-y)(0)$

$\displaystyle \sf \longrightarrow x^3 - y^3=0$

Hence we get required answer.

Answer 2

$\large \underline{ \green{ \boxed{ \bf \blue{Required \: Answer}}}}$

In Attatched File .........