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x² + y² + z² = 9
x³ + y³ + z³ = 24
x² + y² + z² = 9
(x + y + z)² - 2xy - 2xz - 2yz = 9
3² - 2xy - 2xz - 2yz = 9
- 2xy - 2xz - 2yz = 0
xy + xz + yz = 0
= (x² + y² + z²)² - 2x².y² - 2x²z² - 2y²z²
= (9)² - (2x².y² + 2x²z² +2y²z²)
= 81 - (x³ + y³ + z³) - ( xy + xz + yz)
= 81 - 24 - 0
= 57