If x + y + z = 11 , xy + yz + zx = -6 , and x3 + y3 + z3 = 1604, then the value of xyz is :
Answer & explanation
Correct answer: option 1
We know that =
= x³ + y³ + z³ - 3xyz = (x + y + z){(x + y + z)2 - 3(xy + yz + zx)}
= 1604 - 3xyz = 11{121 - 3(- 6)}
= 1604 - 1529 = 3xyz
= xyz = \(\frac{75}{3}\)
= xyz = 25