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Question
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
Solution
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`
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