Let a and b be the solutions to 5x^2 - 11x + 4 = 0. FInd 1/a^2 + 1/b^2.
1/a^2 + 1/b^2 = 13/7.
Try to write $1/a^2+1/b^2$ as an expression involving only $a+b$ and $ab$. The values of $a+b$ and $ab$ can be obtained from the coefficients of $5x^2-11x+4$ almost by inspection. (Vieta)
