Question

If x/y + y/x = -1, x, y # 0, then find the value of x cube - y cube​

Answer 1

Answer:

x³ - y³ = 0

Step-by-step explanation:

$\dfrac{x}{y}+\dfrac{y}{x}=-1\\\\\dfrac{x\cdot x}{y\cdot x}+\dfrac{y\cdot y}{x\cdot y}=-1\\\\\dfrac{x^2}{xy}+\dfrac{y^2}{xy}=-1\\\\\dfrac{x^2+y^2}{xy}=\dfrac{-1}{1}\qquad|\text{cross multipy}\\\\x^2+y^2=-xy\qquad|\text{add}\ xy\ \text{to both sides}\\\\x^2+xy+y^2=0\qquad(*)$

We know:

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

Substitute (*)

$x^3-y^3=(x-y)(0)=0$