#### Question

Solve the following quadratic equations by factorization:

a^{2}b^{2}x^{2} + b^{2}x - a^{2}x - 1 = 0

#### Solution

We have been given

a^{2}b^{2}x^{2} + b^{2}x - a^{2}x - 1 = 0

b^{2}x(a^{2}x + 1) - 1(a^{2}x + 1) = 0

(b^{2}x - 1)(a^{2}x + 1) = 0

Therefore,

b^{2}x - 1 = 0

b^{2}x = 1

`x=1/b^2`

or,

a^{2}x + 1 = 0

a^{2}x = -1

`x=-1/a^2`

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

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#### APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: A2b2x2 + B2x - A2x - 1 = 0 Concept: Solutions of Quadratic Equations by Factorization.