x^2 - 4ax + 4a^2 - b^2 = 0 - Vidyadip

Question

$x^2 - 4ax + 4a^2 - b^2 = 0$

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Answer

$x^2 - 4ax + 4a^2 - b^2 = 0$
$\Rightarrow x^2 - 4ax + (4a^2 - b^2) = 0$
$\Rightarrow x^2 - 4ax + (2a + b)(2a - b) = 0$
$\Rightarrow x^2 - (2a + b)x - (2a - b)x + (2a + b)(2a - b) = 0$
$\Rightarrow x[x - (2a + b)] - (2a - b)[x + (2a + b)] = 0$
$\Rightarrow [x - (2a + b)][x - (2a - b)] = 0$
$\Rightarrow x - (2a + b) = 0 or x - (2a - b) = 0$
$\Rightarrow x = 2a + b or x = 2a - b$

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