Question

$\ \textless \ br /\ \textgreater \ \small\sf \bf \purple{ If \: \frac{x}{y} + \frac{y}{x} = -1 (x, y ≠ 0), then \: find \: the \: value \: of \: x³ – y³ \:}$
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Answer 1

Answer:

$⇒ \frac{x}{y} + \frac{y}{x} = - 1$

$⇒ \frac{ {x}^{2} + {y}^{2} }{yx} = - 1$

$⇒ {x}^{2} + {y}^{2} = - xy$

$⇒ {x}^{2} + xy + {y}^{2} = 0$

$\sf \colorbox{god} {Multiplying both sides by }(x - y)$

$⇒(x - y)( {x}^{2} + xy + {y}^{2} ) = (x - y) \times 0$

$⇒ {x}^{3} - {y}^{3} = 0$

$\[ \left[ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} \right] \]$

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Answer 2

hI tanusreee hru ????