<s>[INST] To find the range of $\sqrt{x-1} + \sqrt{5-x}$ To find the range of $\sqrt{x-1} + \sqrt{5-x}$.
I do not know how to start?
Thanks
 [/INST] Note that
$$
\left(\sqrt{x-1}+\sqrt{5-x}\right)^2=4+2\sqrt{4-(x-3)^2}
$$
Since $4-(x-3)^2\le4$ and $4+2\sqrt{4-(x-3)^2}\ge4$, we get that
$$
2\le\sqrt{x-1}+\sqrt{5-x}\le2\sqrt2
$$
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