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

$={\left(\alpha +\beta \right)}^2-2\alpha \beta +4$

$=25-12+4=17$

$\left({\alpha }^2+2\right)\left({\beta }^2+2\right)={\left(\alpha \beta \right)}^2+2\left({\alpha }^2+{\beta }^2\right)+4$

$=36+2\left(13\right)+4$

$=36+26+4=66$

$\therefore$ $x^2-\left({\alpha }^2+2+{\beta }^2+2\right)x+\left({\alpha }^2+2\right)\left({\beta }^2+2\right)=0$

$x^2-17x+66=0$

                    (or)

$2,3$  are roots of $x^2-5x+6=0$

$2^2+2,3^2+2$  are the roots of

$x^2-\left(2^2+2+3^2+2\right)x+\left(2^2+2\right)\left(3^2+2\right)=0$

$x^2-17x+66=0$