Solve the following quadratic equations by factorization:(a + b)^… - Vidyadip

Question

Solve the following quadratic equations by factorization:$(a + b)^2 x^2 - 4abx - (a - b)^2 = 0$

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Answer

We have been given
$(a + b)^2 x^2 - 4abx - (a - b)^2 = 0$
$(a + b)^2 x^2 - (a + b)^2 x + - (a - b)^2 = 0$
$(a + b)^2 x(x - 1) + (a - b)^2 (x - 1) = 0$
$((a + b)^2 x + (a + b)^2) (x - 1) = 0$
Therefore,
$(a + b)^2 x + (a - b)^2 = 0$
$(a + b)^2 x = -(a - b)^2$
$\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$
or, $x - 1 = 0$
$x = 1$
Hence, $\text{x}=\Big(\frac{\text{a}-\text{b}}{\text{a}+\text{b}}\Big)^2$ or $x = 1$

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