If $m = 2 n + \sqrt{n^{2} + x},$ make $x$ the subject of formula and find the coefficient of $n^{2}$

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Solution

Given, $m = 2 n + \sqrt{n^{2} + x}$
$\Rightarrow m - 2 n = \sqrt{n^{2} + x}$
Squaring both sides, we get
$m^{2} + 4 n^{2} - 4 m n = n^{2} + x$
$\Rightarrow x = m^{2} + 3 n^{2} - 4 m n$

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