Question

If [a+b] 2 = 2a 2 + 2b 2 , show that a=b

Answer 1

Given-
    [a+b]^2 = 2a^2 + 2b^2

Then we have to show that    a=b


Now as we know that -

                           [a+b]^2 = a^2 + 2ab + b^2 --------------------  (i)
so, now according to question 

                            [a+b]^2 = 2a^2 + 2b^2 ------------------------ (ii)

using equation (I) and (ii) we get 
                2a^2 + 2b^2 =  a^2 + 2ab + b^2
         or,        a^2 + b^2    = 2ab
        or, a^2 - 2ab + b^2   = 0
         or,   [a - b]^2           = 0     [using the formula [a-b]^2 = a^2 + 2ab + b^2 ]
so,                        a - b   = 0

Hence                   a = b proved.

Answer 2

(a+b)^2=2a^2+2b^2
a^2+b^2+2ab=2a^2+2b^2
a^2+b^2=2ab
(a-b)^2=0
a-b=0
a=b