Q11 of 39 Page 91

x2 – 4ax + 4a 2 – b 2 = 0. Find the roots of this quadratic equation by the method of completing the square.

Given, x2 – 4ax + 4a2 – b2 = 0


⇒ x2 – 2 × x × 2a + (2a)2 – (2a)2 + 4a2 – b2 = 0


⇒ (x – 2a)2 – b2 = 0


⇒ (x – 2a)2 = b2


⇒ x – 2a = ±b


⇒ x = 2a±b


i. e. x = 2a + b or x = 2a – b


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