Problem find limit

[MR.Perter]

Let [tex]x_{n}[/tex] be a sequence given by [tex]x_{1}=\frac{5}{2}[/tex] and
[tex]x_{n+1}= \sqrt{x_{n}^{3} - 12x_{n} + \frac{20n+21}{n+1}}[/tex] [tex](n\in \mathbb{N^{*}})[/tex]
Prove that the sequence [tex](x_{n})[/tex] converges and find its limit