If x-y-y-x-1 then find x3-y3

The correct option is C 0We know that, x³ y³=(x y)(x²+xy+y²) ........(1) Given that, x/y+y/x= 1 x²+y²/xy= 1 x²+y² = xy Adding xy on both sides, we get x² ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a-b)^3

If x/y+y/x=-1...

Question

If $\frac{x}{y} + \frac{y}{x} = - 1$ then find $x^{3} - y^{3}$

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Solution

The correct option is D 0.0
We know that,
$x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2}) . . . . . . . . (i)$
Given that,
$\frac{x}{y} + \frac{y}{x} = - 1$

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

$\Rightarrow x ² + y ² = - x y$
Adding $x y$ on both sides, we get
$x^{2} + y^{2} + x y = 0 . . . . . . . . . . . (i i)$
on substituting eq.(ii) in eq.(i), we get
$x^{3} - y^{3} = (x - y) (0)$
$∴$ $x^{3} - y^{3} = 0$

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If xy+yx=−1 then find x3−y3

The correct option is D 0.0We know that,x3−y3=(x−y)(x2+xy+y2)........(i) Given that, xy+yx=−1 ⇒x2+y2xy=−1 ⇒x²+y²=−xy Adding xy on both sides, we get x2+y2+xy=0...........(ii)on substituting eq.(ii) in eq.(i), we getx3−y3=(x−y)(0) ∴ x3−y3=0

If $\frac{x}{y} + \frac{y}{x} = - 1$ then find $x^{3} - y^{3}$