If x + y + z = 11 , xy + yz + zx = -6 , and x3 + y3 + z3 = 1604, then the value of xyz is :

25 4 1 5

25

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