The Total solution for NCERT class 6-12
x3 + y3 + z3 –3xyz = (x + y + z) (x2 + y2 + z2 -xy-yz – zx)Now, x + y + z = 8Squaring, we get(x + y + z)2 = (8)2x2 + y2 + z2 + 2(xy + yz+ zx) = 64⇒ x2 +y2 + z2 + 2 x 20 = 64⇒ x2 + y2 + z2 + 40 = 64⇒ x2 + y2 + z2 = 64 – 40 = 24Now,x3 + y3 + z3 – 3xyz = (x + y +z) [x2 + y2 + z2 – (xy + yz +zx)]= 8(24 – 20) = 8 x 4 = 32