Question

$if \: \frac{x}{y} + \frac{y}{x} = (x \: comma \: y \: not \: equal \: to \: 0 \\ find \: value \: of \: {x}^{3} - {y}^{3}$
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Answer 1

$\large\underline{\sf{Solution-}}$

It is given that

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

find the value of

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

So,

From given,

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

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

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

$\sf \: {x}^{2} + {y}^{2} + xy = 0$

On multiply both sides, by x - y,

$\sf \: (x - y)({x}^{2} + {y}^{2} + xy) = 0$

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

Hence,

The value of

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