If x + y + z = 10, xy + yz + zx = 25, xyz = 100, then what is the value of (x³ + y³ + z³ - xyz)?

450

(x + y + z)² = x² + y² + z² + 2 (xy + yz + zx)

100 = x² + y² + z² + 2(25)

⇒ x² + y² + z² = 5

x³ + y³ + z³ - 3xyz = (x + y + z) [x² + y² + z² - (xy + yz + zx)]

⇒ x³ + y³ +z³ - 3xyz = 10 (50 - 25) = 10 (25) = 250

⇒ x³ + y³ +z³ - xyz = 250 + 2xyz

                               = 250 + 2(100) = 250 + 200 = 450