Question

If x/y+y/x=-1 where x is not equal to 0,y is also not equal to 0 then find the value of x^3-y^3

Answer 1

$\rm{\large{\blue{\underline{\underline{Question:-}}}}}$

$\sf{If\: \frac{x}{y} \:+ \:\frac{y}{x} \:= \:-1, \:where\: x \:is \:not\: equal\: to \:0,}$

$\sf{y \:is\: also\: not\: equal\: to\: 0. \:Find \:the\:value}$

$\sf{of \:{x}^{3}\: - \:{y}^{3}}$

$\rm{\large{\green{\underline{\underline{Formula\:used:-}}}}}$

$\tt{{x}^{3}\: -\: {y}^{3}\: = \:(x - y)({x}^{2}\: + \:{y}^{2}\: +\: xy)}$

$\rm{\large{\orange{\underline{\underline{Answer:-}}}}}$

$\sf{\frac{x}{y} \:+ \:\frac{y}{x}\: =\: -1}$

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

$\sf{\rightarrow {x}^{2}\: +\: {y}^{2}\: =\: - xy}$

$\sf{\rightarrow {x}^{3}\: -\: {y}^{3} \:=\: (x \:- \:y)({x}^{2} \:+\: {y}^{2}\: + \:xy)}$

$\sf{\rightarrow {x}^{3}\: - \:{y}^{3}\: =\: (x\: - \:y)(-\: xy\: +\: xy)}$

$\sf{\rightarrow {x}^{3}\: -\: {y}^{3}\: = \:(x \:-\: y)(0)}$

$\sf{\rightarrow {x}^{3}\: -\: {y}^{3}\: = \:0}$