`(a+b)^2= 2(a^2+b^2)`

`<=>a^2+2ab+b^2=2a^2+2b^2`

`<=>2a^2-a^2+2b^2-b^2=2ab`

`<=>a^2+b^2=2ab`

`<=>a^2-2ab+b^2=0`

`<=>(a-b)^2=0`

`<=>a-b=0`

`<=>a=b` (dpcm)

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