Question

If x + y + z = 8 and xy + yz+ zx = 20, find the value of x3 + y3 + z3 – 3xyz.

Answer 1

x + y + z = 8 and xy + yz+ zx = 20.

Squaring, x + y + z = 8 both sides, we get

(x + y + z)2 = (8)2

x2 + y2 + z2 + 2(xy + yz + zx) = 64

x2 + y2 + z2 + 2 x 20 = 64

x2 + y2 + z2 + 40 = 64

x2 + y2 + z2 = 24

Now,

x3 + y3 + z3 – 3xyz = (x + y + z) [x2 + y2 + z2 – (xy + yz + zx)]

= 8(24 – 20)

= 8 x 4 = 32

⇒ x3 + y3 + z3 – 3xyz = 32