If a + b + c = 1, ab + bc + ca = – 1 and abc =

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If a + b + c = 1, ab + bc + ca = – 1 and abc = –1, then the value of a³ + b³ + c³ is :

1. 1
2. –1
3. 2
4. –2

Correct Option: A

a + b + c = 1
ab + bc + ca = –1
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ 1 = a² + b² + c² + 2 (–1)
⇒ a² + b² + c² = 3
∴ a³ + b³ + c³ = 3abc + 4
= –3 + 4 = 1