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If 2(a^2 + b^2) = (a + b)^2 then prove that a = b.

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If 2(a2 + b2) = (a + b)2 then prove that a = b.

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2 (a2 + b2) = (a + b)2

⇒ 2a2 + 2b2 = a2 + 2ab + b2 (Using identity I)

⇒ a2 – 2ab + b2 = 0

⇒ (a – b)2 = 0 (Using identity II)

⇒ a – b = 0

⇒ a = b

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