Question

If x/y +y/x =-1 then the value of x3 -y3 is

Answer 1

Step-by-step explanation:

have you got answer thanks

Answer 2

_________________________________________

$\small\fcolorbox{red}{white}{Given:-}$

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

$\small\fcolorbox{red}{white}{To find:-}$

${x}^{3} - {y}^{3}$

_________________________________________

$\small\fcolorbox{red}{white}{Solution:-}$

$\: \: \: \: \: \: \: \: \: \frac{x}{y} + \frac{y}{x} = - 1 \\ \\ = > \frac{ {x}^{2} + {y}^{2} }{xy} = - 1 \\ \\ = > {x}^{2} + {y}^{2} = - xy......(i)$

_________________________________________

Now,

$\: \: \: \: \: \: {x}^{3} - {y}^{3} \\ \\ = (x - y)( {x}^{2} + {y}^{2} + xy) \\ \\ = (x - y)( - xy + xy) \: \: \: \: \: \: \: \: - - \: (from \: (i) \: \: ) \\ \\ = (x - y) \times 0 \\ \\ = 0$

_________________________________________