1. Given that $\alpha, \beta$ are the roots of the equation $x^{2}-7 x+8=0$, and $\alpha$ $>\beta$. Without solving the equation, use the relationship between roots and coefficients to find the value of $\frac{2}{\alpha}+3 \beta^{2}$.
(8th "Zu Chongzhi Cup" Mathematics Invitational Competition)
(Tip: Construct a conjugate. Answer: $\frac{1}{8}(403-85 \sqrt{17})$ )