Having trouble with this question, any help will be appreciated, thanks.

Let x be a positive number, with $\displaystyle x^2>2.$

Let $\displaystyle y = x/2 + 1/x$

Show that $\displaystyle 0<y<x$, and that $\displaystyle y^2>2$. Explain why this shows that there is no smallest positive number whoes square is more than 2.