Question

if 2x= a+b+c
show that

(x-a)² + (x-b)² + (x-c)² + x² = a² + b² + c²

Answer 1

here is solution all the 2 are cancelled. please ask about any doubt or something

Answer 2

Hello,

$\boxed{(x-a)^2+(x-b)^2+(x-c)^2+x^2}\ \\ =(x^2-2ax+a^2)+(x^2-2bx+b^2)+(x^2-2cx+c^2)+\ x^2\\ =3x^2-2x(a+b+c)+x^2+a^2+b^2+c^2\\ =3x^2-4x^2+x^2+a^2+b^2+c^2\\ =\boxed{a^2+b^2+c^2}$