Q. 11

# x^{2} – 4ax + 4a ^{2} – b ^{2} = 0. Find the roots of this quadratic equation by the method of completing the square.

Answer :

Given, x^{2} – 4ax + 4a^{2} – b^{2} = 0

⇒ x^{2} – 2 × x × 2a + (2a)^{2} – (2a)^{2} + 4a^{2} – b^{2} = 0

⇒ (x – 2a)^{2} – b^{2} = 0

⇒ (x – 2a)^{2} = b^{2}

⇒ x – 2a = ±b

⇒ x = 2a±b

i. e. x = 2a + b or x = 2a – b

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