If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a...

Now, ${a}^{2} + {b}^{2} + {c}^{2} = {\left(a + b + c\right)}^{2} - 2Σab = - 3$

$⇒ {\left(ab + bc + ca\right)}^{2} = Σ{\left(ab\right)}^{2} + 2abcΣa$

$⇒ Σ{\left(ab\right)}^{2} = - 2$

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

$= 9 - 2\left(- 2\right)$

$= 13 .$