If $x = - 2$ and $x^{2} + y^{2} + 3 x y = - 5$

- 2

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3

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4

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None of these

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Solution

The correct option is B $3$
$x^{2} + y^{2} + 3 x y = - 5$
Substitute $x = - 2$ ,
$\Rightarrow$ $(- 2)^{2} + y^{2} + 3 (- 2) y = - 5$
$\Rightarrow$ $4 + y^{2} - 6 y = - 5$
$\Rightarrow$ $y^{2} - 6 y + 9 = 0$
$\Rightarrow$ $y^{2} - 3 y - 3 y + 9 = 0$
$\Rightarrow$ $y (y - 3) - 3 (y - 3) = 0$
$\Rightarrow$ $(y - 3) (y - 3) = 0$
$\Rightarrow$ $y - 3 = 0$ and $y - 3 = 0$
$∴$ $y = 3, 3$

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