# Just $$m$$

Algebra Level 5

$\large \sqrt{x+1}+\sqrt{3-x}+2\sqrt{(x+1)(3-x)}\leq m+1$ If there exist a range of $$m$$ that makes the above inequality holds true for all $$x$$, find the minimum value of $$m$$ in that range.

*Note: if you think there are no range exist or that range have the form $$(\alpha;\beta$$); submit your answer as $$1.11$$