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