Question

If $a+b+c=9$ and $ab+bc+ca=23$, find the value of $a^2+b^2+c^2.$

Answer 1

Given, $a+b+c=9,ab+bc+ca=23$

Using identity,
$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$
$\Rightarrow (9{)}^2=a^2+b^2+c^2+2(ab+bc+ca)$
$\Rightarrow 81=a^2+b^2+c^2+2\left(23\right)$
$\Rightarrow 81=a^2+b^2+c^2+46$
$\Rightarrow a^2+b^2+c^2=81-46$
$\therefore a^2+b^2+c^2=35$

Hence, the value of $a^2+b^2+c^2$ is $35$.