Mathematics - Quadratic Equation Question with Solution | TestHub

We have,$a+b+c=1,ab+bc+ca=2$and$abc=3$

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

$\Rightarrow {\left(ab+bc+ca\right)}^2=\Sigma {\left(ab\right)}^2+2abc\Sigma \mathrm{a}$

$\Rightarrow \Sigma {\left(ab\right)}^2=-2$

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

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

$=13.$