If x + y + z = 11
xy + yz + zx = -6
x3 + y3 + z3 = 1604
find xyz
Answer & explanation
Correct answer: option 2
(x + y + z)2 = x2 + y2 + z2 + 2 (xy + yz + zx)
(11)2 = x2 + y2 + z2 + 2 × -6
x2 + y2 + z2 = 121 + 12 = 133
⇒ x3 + y3 + z3 – 3xyz = (x + y + z)[( x2 + y2 + z2) – (xy + yz + zx)
1604 – 3xyz = 11 [133 – (-6)]
3xyz = 1604 – 1529
xyz = 25