Question

P and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)

Answer 1

1) Let's find the roots of the equation: 5x² -7x +1

5x² -7x +1

2) Calling x_1 =p and x_2= q

Plugging them into the (p/q)+(q/p)​ expression, dividing the fractions. And then rationalizing it we'll have finally:

`\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}(39)/(5)`