Đáp án:
$ x=3-2\sqrt{3}$
Giải thích các bước giải:
Dkdx: $-1\le x\le 7$
$\sqrt{x+1}+\sqrt{7-x}=3-x$
$\rightarrow \sqrt{x+1}+\sqrt{7-x}=\dfrac{1}{2}((7-x)-(x+1))$
$\rightarrow \sqrt{x+1}+\sqrt{7-x}=\dfrac{1}{2}.(\sqrt{x+1}+\sqrt{7-x}).(\sqrt{7-x}-\sqrt{x+1})$
$\rightarrow \sqrt{7-x}-\sqrt{x+1}=2$
$\rightarrow \sqrt{7-x}-\sqrt{x+1}+\sqrt{7-x}+\sqrt{x+1}=3-x+2$
$\rightarrow 2\sqrt{7-x}=7-x-2$
$\rightarrow 7-x-2\sqrt{7-x}-2=0$
$\rightarrow \sqrt{7-x}=1+\sqrt{3}$
$\rightarrow x=3-2\sqrt{3}$