If $x + y + z = 0$ , then $x^{3} + y^{3} + z^{3}$ = ..........

3 x y z

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x^{2} y z

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x y^{2} z

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x y z^{2}

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Solution

The correct option is A $3 x y z$
$x + y + z = 0 \Rightarrow x + y = - z$
Cubing on both sides,
$(x + y)^{3} = (- z)^{3}$
$\Rightarrow x^{3} + y^{3} + 3 x y (x + y) = z^{3}$
$\Rightarrow x^{3} + y^{3} + 3 x y (- z) = - z^{3}$
$\Rightarrow x^{3} + y^{3} - 3 x y z + z^{3} = 0$
$∴ x^{3} + y^{3} + z^{3} = 3 x y z$

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Similar questions

x^{3} + y^{3} + z^{3} = 3 x y z

x + y + z = ?

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x^{3} + y^{3} + z^{3} = 3 x y z

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x^{3} + y^{3} + z^{3} = 3 x y z .

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