Interpret this geometrically, as a statement about parallelograms.

[Jamin2112]

Homework Statement

Prove that

|x+y|² + |x-y|² = 2|x|² + 2|y|²

if x and y are elements of ℝ^k

Homework Equations

Ordinary stuff

The Attempt at a Solution

Got the first part, but I don't understand the parallelogram thing yet. The little sketch I drew didn't help.

 

[vrmuth]

In a parallelogram the sum of squares of sides equals the sum of squares of its diagonals

 

[vrmuth]

Prove that

|x+y|² + |x-y|² = 2|x|² + 2|y|²

if x and y are elements of ℝ^k

since $\left|X+Y\right|$ and $\left|X-Y\right|$ are diagonals of the parallelogram with $\left|X\right|$and $\left|Y\right|$ as the sides , it states the property
"In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"

 

[Jamin2112]

since $\left|X+Y\right|$ and $\left|X-Y\right|$ are diagonals of the parallelogram with $\left|X\right|$and $\left|Y\right|$ as the sides , it states the property
"In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"

Drew the picture again. Now I understand it. Indeed: On a parallelogram, the sum of squares of diagonals equals the sum of squares of the sides