Question

if x/y +y/x = -1 .find value of x^3-y^3

Answer 1

hey mate,

we know that,


${x}^{3} - {x}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )........(1) \\ given \: that \: \\ \frac{x}{y} + \frac{x}{y} = - 1 \\ {x}^{2} + {y}^{2} = - xy \\ {x}^{2} + {y}^{2} + xy = 0 \\ ( {x}^{2} + xy + {y}^{2} ) = 0 \\ multiplyig \: by( x - y) \: on \: both \: side \\ we \: get \: \\ (x - y)( {x}^{2} + xy + {y)}^{2} ) \\ = (x - y) \times 0 \\ by \: equal \: we \: get \\ {x}^{2} + {y}^{2} = 0 \\ hence \: {x}^{2} - {y}^{2} = 0$
I hope this helps you!
@vaibhav246