If $x + y + z = 1, xy + yz + zx = -26$ and $x^3 + y^3 + z^3 = 151$, then what will be the value of $xyz$?
Answer & explanation
Correct answer: option 1
x + y + z = 1,
xy + yz + zx = – 26,
x3 + y3 + z3 = 151
x3 + y3 + z3 – 3xyz = (x + y + z)[(x + y + z)2 – 3 (xy + yz + zx)]
= 151 – 3xyz = 1 [12 – 3 × ( – 26)]
= 151 – 3xyz = 1 + 78 = 79
= 3xyz = 151 – 79 = 72
= xyz = 24