Question
Solve the following quadratic equation:$x^2 - 2ax - (4b^2 - a^2) = 0$
✓
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 $x = a + 2b$
$\Rightarrow x^2 - 2ax + (a^2 - 4b^2) = 0$
$\Rightarrow x^2 - 2ax + (a - 2b)(a + 2b) = 0$
$\Rightarrow x^2 - (a - 2b)x - (a + 2b)x + (a - 2b)(a + 2b) = 0$
$\Rightarrow x[x + (a - 2b)] - (a + 2b)[x - (a - 2b)] = 0$
$\Rightarrow [x - (a - 2b)][x - (a + 2b)] = 0$
$\Rightarrow x - (a - 2b) = 0$ or $x - (a + 2b) = 0$
$\Rightarrow x = a - 2b$ or $x = a + 2b$
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