回復 13# 王保丹 的帖子
令\(a+1=x , b+3=y\)
則原式=\(\displaystyle\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x+y}}\)
設\(f(x) = \sqrt x \)
由jensen不等式，對於\(x,y > 0\)
則有\(\displaystyle\sqrt {\frac{{x + y}}{2}} \ge \frac{1}{2}(\sqrt x + \sqrt y )\)
即\(\displaystyle\frac{{\sqrt x + \sqrt y }}{{\sqrt {x + y} }} \le \frac{2}{{\sqrt 2 }} = \sqrt 2 \)
