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If x + y + z = 1, 1 + 1 + 1 = 1 and xyz = – 1, then x³ + y³ + z³ is equal to x y z
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- –1
- 1
- –2
- 2
Correct Option: B
x + y + z = 1 ..... (i)
Again,
| + | + | = | = 1 | |||||
| x | y | z | xyz |
⇒ xy + yz + zx = xyz = –1 .. (ii)
∴ (x + y + z)² = x² + y² + z² + 2 (xy + yz + zx)
⇒ 1 = x² + y² + z² – 2
⇒ x² + y² + z² = 2 + 1 = 3 .(iii)
∴ x³ + y³ + z³ – 3xyz
= (x + y + z) (x² + y² + z² – xy – yz – zx)
= 1 (3 + 1) = 4
⇒ x³ + y³ + z³ + 3 = 4
⇒ x³ + y³ + z³ = 4 – 3 = 1
