If $a+b+c=9$ and $ab+bc+ca=26$, find $a^2+b^2+c^2$

$\begin{array}{l}{(a+b+c)}^2=a^2+b^2+c^2+2ab+2bc+2ca\\ \Rightarrow {(a+b+c)}^2=(a^2+b^2+c^2)+2(ab+bc+ca)\\ \Rightarrow 9^2=(a^2+b^2+c^2)+2\left(26\right)\end{array}$

[Putting the value of $a+b+candab+bc+ca$]

$\begin{array}{l}\Rightarrow 81=(a^2+b^2+c^2)+52\\ \Rightarrow (a^2+b^2+c^2)=81-52=29\end{array}$