If x + y + z = 2, xy + yz + zx = -11, and xyz = -12, then what is the value of x3 +y3 +z3 ?
Answer & explanation
Correct answer: option 2
x3 + y3 + z3 – 3xyz = (x + y +z) [(x + y + z)2 – 3(xy + yz + zx)]
= x3 + y3 + z3 – 3 × (–12) = 2[22 – 3 × (– 11)]
= x3 + y3 + z3 + 36 = 2[4 + 33]
= x3 + y3 + z3 + 36 = 2 × 37
= x3 + y3 + z3 = 74 – 36 = 38