Prove that the monic polynomials $Q_{n}, n \geq 0$, orthogonal with respect to a given weight function $w(x)>0$ on $[a, b]$, satisfy the three-term recurrence relation

$$Q_{n+1}(x)=\left(x-a_{n}\right) Q_{n}(x)-b_{n} Q_{n-1}(x), \quad n \geq 0$$

where $Q_{-1}(x) \equiv 0, Q_{0}(x) \equiv 1$. Express the values $a_{n}$ and $b_{n}$ in terms of $Q_{n}$ and $Q_{n-1}$ and show that $b_{n}>0$.