Question

Solve the following quadratic equations by factorization:

(a + b)²x² - 4abx - (a - b)² = 0

Answer 1

We have been given

(a + b)²x² - 4abx - (a - b)² = 0

(a + b)²x² - (a + b)²x + (a - b)2x - (a - b)² = 0

(a + b)²x(x - 1) + (a - b)²(x - 1) = 0

((a + b)²x + (a - b)²)(x - 1) = 0

Therefore,

(a + b)²x + (a - b)² = 0

(a + b)²x = - (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