Find the roots
$x^{2} - 4 a x + 4 a^{2} - b^{2} = 0$

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Solution

$x^{2} - 4 a x + 4 a^{2} - b^{2} = 0$ roots will be given by
$x = \frac{4 a \pm \sqrt{(4 a)^{2} - 4 (4 a^{2} - b^{2})}}{2}$

$= \frac{4 a \pm \sqrt{16 a^{2} - 16 a^{2} + 4 b^{2}}}{2}$

$= \frac{4 a \pm 2 b}{2}$

$x = 2 a + b$ , $2 a - b$ .

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x^{2} - 4 a x + 4 a^{2} - b^{2} = 0

x^{2} - 4 a x + 4 a^{2} - b^{2} = 0 .

x^{2} - 4 a x + 4 a^{2} - b^{2} = 0

x^{2} - 4 a x + 4 a^{2} - b^{2} = 0

x^{2} - 4 a x + 4 a^{2} - b^{2} = 0

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