If a + b + c = 26 and ab + bc + ca = 109, find the value of a2 + b2 + c2 = ?

Answer: Option A

$$\begin{array}{rl}& {\left(a+b+c\right)}^2=a^2+b^2+c^2+2\left(ab+bc+ca\right)\\ & \Rightarrow {\left(26\right)}^2=a^2+b^2+c^2+2\left(109\right)\\ & \Rightarrow a^2+b^2+c^2=676-218\\ & \Rightarrow a^2+b^2+c^2=458\end{array}$$