Question

solve the given Question:-

Answer 1

Solution :

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Given :

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

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To find :

The value of x³ - y³

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If,

⇒ $\frac{x}{y} + \frac{y}{x} = -1$

Then,

⇒ $\frac{x}{y} + \frac{y}{x} = -1$

⇒ $\frac{x^2 + y^2}{xy}= -1$

⇒ $x^2 + y^2= (xy)(-1)$

⇒ $x^2 + y^2 = -xy$

⇒ x² + y² + xy = 0 ......(i)

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We know the identity that,

⇒ a³ - b³ = (a - b)(a² + ab + b²)

Hence,

Let
 
⇒ a = x

⇒ b = y,.

Then,

⇒ x³ - y³ = (x - y)(x² + xy + y² )

From equation (i) we get,

⇒ x³ - y³ = (x - y)(0)

⇒ x³ - y³ = 0,..

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                                            Hope it Helps !!

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