Question

If x/y+y/x=-1 then find x^3-x^3

Answer 1

$\huge\textbf{Solution}$
$<I>$
$The \: given \: equation \: is \: \: \dfrac{x}{y} + \dfrac{y}{x} = - 1 \\ \\ \frac{ {x}^{2} + {y}^{2} }{xy} = - 1 \\ \\ {x}^{2} + {y}^{2} = - xy - - - - - - - (1)$
We know that


x³- y³= (x - y)(x²+ xy + y²)


$\textbf{So consider this identity}$


x³- y³= (x - y)(x²+ xy + y²)


= (x - y)(x² + y² + xy )


= (x - y)(-xy +xy) [ x² + y² = -xy (from equation 1) ]


= (x - y)(0)


= 0

Thanks

Have a colossal day ahead

Be Brainly