Question

Solve the following quadratic equations by factorization:

4x² + 4bx – (a² – b²) = 0

Answer 1

4x² + 4bx - (a² - b²) = 0

4x² + 2(a + b)x - 2(a - b)x - (a² - b²) = 0

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

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

Therefore,

2x - (a - b) = 0

2x = a - b

`x=(a-b)/2`

or,

2x + a + b = 0

2x = -(a + b)

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

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