46
If x + y + z = 6 and x2 + y2 + z2 = 20 then the value of x3 + y3 + z3 – 3xyz is
- A64
- B70
- C72
- D76
Answer not set
Discussion 1
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CCommunity
Given, x + y + z = 6 and x2 + y2 + z2 = 20
We know the identity:
⇒ (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
Hence, 62 = 20 + 2(xy + yz + zx)
∴ xy + yz + zx = 8
We know the identity:
⇒ x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz - zx)
= 6 × (20 – 8)
= 6 × 12
= 72
We know the identity:
⇒ (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
Hence, 62 = 20 + 2(xy + yz + zx)
∴ xy + yz + zx = 8
We know the identity:
⇒ x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz - zx)
= 6 × (20 – 8)
= 6 × 12
= 72