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If 4x2+ y2 ...

Question

If $4 x^{2} + y^{2} = 40$ and $x y = 6$ , find the value of $2 x + y$

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Solution

We have,
$(2 x + y)^{2} = (2 x)^{2} + y^{2} + 2 \times 2 x \times y$

$\Rightarrow (2 x + y)^{2} = (4 x^{2} + y^{2}) + 4 x y$

$\Rightarrow (2 x + y)^{2} = 40 + 4 \times 6 \Rightarrow (2 x + y)^{2} = 64$

$\Rightarrow 2 x + y = \pm \sqrt{64} \Rightarrow 2 x + y = \pm 8$

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