\sqrt{2x^{2}+4x+3}+\sqrt{x^{2}+2x+5}=-x^{2}-2x+2 \Leftrightarrow \sqrt{2(x+1)^{2}+1}+\sqrt{(x+1)^{2}+4}=-(x+1)^{2}+3
vì 2(x+1)^{2}+1\geq 1\Rightarrow \sqrt{2(x+1)^{2}+1}\geq \sqrt{1}=1
(x+1)^{2}+4\geq 4\Rightarrow \sqrt{(x+1)^{2}+4}\geq \sqrt{4}=2
lại có -(x+1)^{2}+3\leq 3
VT\geq 3 ; VP\leq 3...