If $x + y + z = 0$ , then $x^{2} + x y + y^{2}$ equals:

y^{2} + y z + z^{2}

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y^{2} - y z + z^{2}

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z^{2} - x y

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z^{2} + z x + x^{2}

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Solution

The correct option is C $z^{2} - x y$
$x + y + z = 0$
$\Rightarrow x + y = - z$
$∴ x^{2} {+ x y + y}^{2} = x^{2} {+ 2 x y + y}^{2} - x y$
$= {(x + y)}^{2} - x y = {(- z)}^{2} - x y = z^{2} - x y$

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