Solve the following quadratic equation:x^2 - 2ax - (4b^2 - a^2) =… - Vidyadip

Question

Solve the following quadratic equation$:x^2 - 2ax - (4b^2 - a^2) = 0$

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Answer

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

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