Question

x/y+y/x=-1,then find the value of x^3-y^3

Answer 1

Given Equation is $\frac{x}{y} + \frac{y}{x} = -1$

LCM is xy.

$\frac{x^2+y^2}{xy} = -1$

x^2 + y^2 = -xy  ---- (1).


We know that a^3 - b^3 = (a-b)(a^2+ab+b^2)

Then x^3-y^3 = (x+y)(x^2+xy+y^2)

                       = (x+y)(-xy+xy)(From (1))

                       = (x+y)(0)

                       = 0.


Therefore x^3 - y^3 = 0.


Hope this helps!