Question

nosso online
1) a) prove that (x+y)² + (x-y)² = 2(x)² + 2(y)2
x€Rk and y€Rk interpret
germanically as a statement about parallelogram
​

Answer 1

It's easy. Check it out.

Given to prove:-

• ${(x + y)}^{2} + {(x - y)}^{2} = 2 {x}^{2} + 2 {y}^{2}$

Solution:-

Simplifying Left Hand Side, we get,

${(x + y)}^{2} +{ (x - y)}^{2}$

$= {x}^{2} + 2xy + {y}^{2} + {x}^{2} - 2xy + {y}^{2}$

$= {x}^{2} + {x}^{2} + {y}^{2} + {y}^{2} + \cancel{2xy} - \cancel{2xy}$

$= 2 {x}^{2} + 2 {y}^{2}$

Simplifying RHS, we get,

$2 {x}^{2} + 2 {y}^{2}$

Therefore,

LHS = RHS (Proved).