Help Algebra

Here : https://web2.0calc.com/questions/algebra_39593

Simplify, getting ${x}^{2}-23x+17=0$. We what to find $\frac{1}{{a}^{2}}+\frac{1}{{b}^{2}}=\frac{{b}^{2}+{a}^{2}}{{(ab)}^{2}}$.

We see that what we want simplfies into $\frac{(a+b)^2-2ab}{(ab)^2}$. By vieta's this is $\frac{{23}^{2}-2*17}{{17}^{2}}=\frac{495}{289}$.