I'm having trouble working out this question. Could someone please provide working on how to solve this.

If $\displaystyle 2x = a + b + c$, show that $\displaystyle (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2$

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- Feb 3rd 2008, 11:17 PMacevipaMaths Question
I'm having trouble working out this question. Could someone please provide working on how to solve this.

If $\displaystyle 2x = a + b + c$, show that $\displaystyle (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = a^2 + b^2 + c^2$ - Feb 3rd 2008, 11:46 PMmr fantastic
- Feb 4th 2008, 12:20 AMmr fantastic
And elegant:

$\displaystyle (x-a)^2 + (x-b)^2 + (x-c)^2 + x^2 = x^2 - 2ax + a^2 + x^2 - 2bx + b^2 + x^2 - 2cx + c^2 + x^2$

$\displaystyle = a^2 + b^2 + c^2 + 4x^2 -2x(a + b + c)$.

Substitute $\displaystyle a + b + c = 2x$:

$\displaystyle = a^2 + b^2 + c^2 + 4x^2 -4x^2 = a^2 + b^2 + c^2 $.

Let your mood decide which way is for you.