Q59 / 90 · JEE Main 2021 (25 Jul Shift 2) · Mathematics

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:

Correct answer: 13

Solution

We have,

a + b + c = 1, a b + b c + c a = 2

and

a b c = 3

Now, $a^{2} + b^{2} + c^{2} = {(a + b + c)}^{2} - 2 Σ a b = - 3$

$\Rightarrow {(a b + b c + c a)}^{2} = Σ {(a b)}^{2} + 2 a b c Σ a$

$\Rightarrow Σ {(a b)}^{2} = - 2$

So, $a^{4} + b^{4} + c^{4} = {(a^{2} + b^{2} + c^{2})}^{2} - 2 Σ {(a b)}^{2}$

$= 9 - 2 (- 2)$

$= 13 .$

Hence, the correct answer is 13.