real numbers, question 4, grade 9

20/06/2016

4)

Given:  $x=\sqrt5+1\,\,and\,y =\sqrt5-1$

a) Calculate  ${x^2}\&{y^2}\,$

b) Prove by using the previous results that  $\frac{x}{y}+\frac{y}{x}$ is a natural number.