[tex]\begin{cases}a_2=a_1+d\\a_3=a_1+2d\end{cases}\Rightarrow \begin{cases}a_1+a_2+a_3=27\\ a_1^2+a_2^2+a_3^2=275\end{cases}\Leftrightarrow \begin{cases}a_1+a_1+a_1+d+2d=27\\a_1^2+\left ( a_1+d \right )^2+\left ( a_1+2d \right )^2=275\end{cases}\Leftrightarrow \\\Leftrightarrow \begin{cases}3a_1+3d=27\\a_1^2+\left ( a_1+d \right )^2+\left ( a_1+2d \right )^2=275\end{cases}\Leftrightarrow \begin{cases}a_1=9-d\\(9-d)^2+18d+d^2+81+81-275=0\end{cases}\Leftrightarrow[/tex][tex]\\\Leftrightarrow \begin{cases}a_1=9-d\\2d^2-23=0\end{cases}\Leftrightarrow \begin{cases}a_1=9-d\\d^2=16\end{cases}\Rightarrow d=4\Rightarrow a_1=5\Rightarrow a_3=5+8=13[/tex]