Question

verify that xcube+ycube+zcube-3xyz=[x+y+z](x-y)wholesq+(y-z)wholesq+(z-x) wholesq​

Answer 1

Step-by-step explanation:

solving R.H.S

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

1/2(x+y+z)(x2+y2-2xy+y2+z2-2yz+z2+x2-2zx)

1/2(x+y+z)(2x2+2y2+2z2-2xy-2yz-2zx)

1/2(x+y+z)(2)(x2+y2+z2-xy-yz-xz)

(x+y+z)(x2+y2+z2-xy-yz-zx)

we know x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx)

=L.H.S

Hence proved