If a + b + c = 1 , a b + b c + c a = 2 and a b c = 3 , then the value of a 4 + b 4 + c 4 is equal to:

Question

If a + b + c = 1 , a b + b c + c a = 2 and a b c = 3 , then the value of a 4 + b 4 + c 4 is equal to:,

MARKS App · Accepted Answer

We have, a + b + c = 1 , a b + b c + c a = 2 and a b c = 3 Now, a 2 + b 2 + c 2 = a + b + c 2 - 2 Σ a b = - 3 ⇒ a b + b c + c a 2 = Σ a b 2 + 2 a b c Σ a ⇒ Σ a b 2 = - 2 So, a 4 + b 4 + c 4 = a 2 + b 2 + c 2 2 - 2 Σ a b 2 = 9 - 2 - 2 = 13 .

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