Question

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Answer 1

QUESTION:-

$\sf\;If\;\frac{x}{y}+\frac{y}{x}=-1\;then\;find\;the\;value\;of\;x^3-y^3$

EXPLANATION:-

$\sf\;\frac{x}{y}+\frac{y}{x}=-1\\\\Taking\;lcm\;and\;solvving\;we\;get:-\\\frac{x^2+y^2}{xy}=-1\\\\x^2+y^2=-xy\\\\x^2+y^2+xy=0 \;\;By\;transposing$

We know x³-y³=(x-y)(x²+xy+y²)

Since here (x²+xy+y²)=0

x³-y³=(x-y)(0)

x³-y³=0

So the value of x³-y³ is 0