Given (a-b)^2 = 2(a^2+b^2)
We know that, (a-b)^2 = a^2 + b^2 - 2ab
So given equation can be written like this
a^2 + b^2 - 2ab = 2(a^2 + b^2)
a^2 + b^2 - 2ab = 2a^2 + 2b^2
-2ab = a^2 + b^2
a^2 + b^2 + 2ab = 0
(a+b)^2 = 0 ( ∵ (a+b)^2 = a^2 + b^2 + 2ab)
a + b = 0
a = -b
Hence its proved
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