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Question
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
Solution
We have, x2 – 2ax + (a2 – b2) = 0
⇒ x2 – ((a + b) + (a – b))x + (a2 – b2) = 0
⇒ x2 – (a + b)x – (a – b)x + (a + b)(a – b) = 0 ......[∵ a2 – b2 = (a + b)(a – b)]
⇒ x(x – (a + b)) – (a – b)(x – (a + b)) = 0
⇒ (x – (a + b))(x – (a – b) = 0
⇒ x = a + b, a – b
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