If $4 x^{2} + y^{2} = a$ and $x y = b$ , find the value of $2 x + y$ .

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Solution

$4 x^{2} + y^{2} = a$ and $x y = b$
$4 x^{2} + 4 x y + y^{2} = a + 4 b$
$⟹ (2 x + y)^{2} = a + 4 b$
$⟹ 2 x + y = \sqrt{a + 4 b}$

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