Question

Show that if 2(a^2 + b^2) = ( a+b)^2 , then a=b

Answer 1

as ,
2( a² + b² ) = ( a + b ) ²

=> 2a² + 2b² = a² + b² + 2ab

=> 2a² - a² + 2b² - b² = 2ab

=> a²+b² = 2ab

=> (a²+b²-2ab) = 0

=> (a-b)² = 0

=> ( a - b ) = 0

=> a = b


hence proved


this can checked also ,

as

a = b

=> 2 (a²+a²) = (a+a)²


=> 2 ( 2a²) = (2a) ²

=> 4a² = 4a²
this is the check.



hope this helps

Answer 2

$2(a { }^{2} + b {}^{2} ) = (a + b) {}^{2} \\ 2(a {}^{2} + b {}^{2} ) = a {}^{2} + b {}^{2} + 2ab \\ 2a {}^{2} + 2b {}^{2} =a { }^{2} + b {}^{2} + 2ab \\ a {}^{2} + b {}^{2} = 2ab \\ a {}^{2} + b {}^{2} - 2ab = 0 \\( a - b) {}^{2} = 0 \\ (a - b) = 0 \\ a = b$
Hence, Proved.