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:

If a+b+c=1,ab+bc+ca=2 and abc=3, then the value of a4+b4+c4 is equal to:

Solution

We have, a+b+c=1,ab+bc+ca=2 and abc=3

Now, a2+b2+c2=a+b+c2-2Σab=-3

⇒ab+bc+ca2=Σab2+2abcΣa

⇒Σab2=-2

So, a4+b4+c4=a2+b2+c22-2Σab2

=9-2-2

=13.

Asked in: JEE Main 2021 (25 Jul Shift 2)

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