#### Question

Solve the following quadratic equations by factorization:

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

#### Solution

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)2x - (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}

`x=-((a-b)/(a+b))^2`

or,

x - 1 = 0

x = 1

Hence, `x=-((a-b)/(a+b))^2` or x = 1

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#### APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: (A + B)2x2 - 4abx - (A - B)2 = 0 Concept: Solutions of Quadratic Equations by Factorization.