- #1

SithsNGiggles

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## Homework Statement

I had this posted under a different question a while back and didn't get any responses, so I thought I'd rephrase it. I've reduced it to what I think I'm supposed to show. (Here's the old post: https://www.physicsforums.com/showthread.php?p=4260206#post4260206 ... Disregard the actual coefficients, I fudged those a bit.)

## Homework Equations

## The Attempt at a Solution

I have to show the following:

##||x||^2 = \frac{2}{3}|x_1|^2+\frac{1}{6}|x_1-\sqrt3x_2|^2+\frac{1}{6}|x_1+\sqrt3x_2|^2##

##x\in\mathbb{R}^2##, so ##x=(x_1,x_2)##, and the left side can be rewritten so that I have

##|x_1|^2+|x_2|^2 = \frac{2}{3}|x_1|^2+\frac{1}{6}|x_1-\sqrt3x_2|^2+\frac{1}{6}|x_1+\sqrt3x_2|^2##

Is there any way to do this?