If x + y + z = 6 and x2 + y2 + z2= 20 then the value of

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If x + y + z = 6 and x² + y² + z²= 20 then the value of x³ + y³ + z³ – 3xyz is

1. 64
2. 70
3. 72
4. 76

Correct Option: C

x + y + z = 6
On squaring,
x² + y² + z² + 2xy + 2zy + 2zx = 36
⇒ 20 + 2 (xy + yz + zx) = 36
⇒ xy + yz + zx = 8
∴ x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)
= 6 (20 – 8)
= 72