Question

if x/y + y/x equal to 1 ,then find the value of x3 -y3

Answer 1

Here's your answer !!

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

$= > \frac{ {x}^{2} + {y}^{2} }{xy} = 1$

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

We know that,

$= > ( {x}^{3} + {y}^{3}) = (x - y)(x {}^{2} + {y}^{2} + xy )$

By putting value of x^2 +y^2 ,we get :-

$= > ({x}^{3} - {y}^{3} ) = (x - y)( - xy + xy)$

$- xy \: and \: xy \: get \: cancelled$

$= > ({x}^{3} - y ^{3}) = (x - y)(0)$

$= > ( {x}^{3} - {y}^{3}) = 0$

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Hope it helps you !! :)