Question

Verify that x³+y³+z³-3xyz=1/2(x +y +z) [(x-y)²+(y -z)²+(z -x)²]

Answer 1

Answer:

Taking R.H.S (right hand side)

1/2(x+y+z)((x-y)^2+(y-z)^2+(x-z)^2)

1/2(x+y+z)(x^2+y^2-2xy+y^2+z^2-2yz+x^2+z^2-2xz)

1/2(x+y+z)(2x^2+2y^2+2z^2-2xy-2yz-2xz)

1/2(x+y+z)2(x^2+y^2+z^2-xy-yz-xz)

(x+y+z)(x^2+y^2+z^2-xy-yz-xz)

Hence proved.

L.H.S=R.H.S