If $\alpha ,\beta$ are the roots of the equation $x^2-5x+6=0$ then the equation whose roots ${\alpha }^2+2 and {\beta }^2+2$ is

$$\begin{gathered} {\alpha }^2+2+{\beta }^2+2={\alpha }^2+{\beta }^2+4 \\ ={(\alpha +\beta )}^2-2\alpha \beta +4 \\ =25-12+4=17 \\ ({\alpha }^2+2)({\beta }^2+2)={\left(\alpha \beta \right)}^2+2({\alpha }^2+{\beta }^2)+4 \\ =36+2\left(13\right)+4 \\ =36+26+4=66 \\ \therefore x^2-({\alpha }^2+2+{\beta }^2+2)x+({\alpha }^2+2)({\beta }^2+2)=0 \\ {x}^2-17x+66=0 \\ \left(or\right) \\ 2, 3 are roots of x^2-5x+6=0 \\ {2}^2+2,3^2+2 are the roots of \\ {x}^2-(2^2+2+3^2+2)x+(2^2+2)(3^2+2)=0 \\ {x}^2-17x+66=0 \end{gathered}$$