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Question
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solution
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R
⇒ 4x2 - {2(a + b)x + 2(a - b)x} + 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
⇒ 2x - (a + b) = 0
or
2x - (a - b) = 0
⇒ x = `(a + b)/(2)` or x = `(a - b)/(2)`.
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