+1537 Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 + 12x - 13. Find 1/a^2 + 1/b^2.
+399 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 \(\frac{{23}^{2}-2*17}{{17}^{2}}=\frac{495}{289}\).
