If $x$ and $y$ are nonnegative real numbers such that $x+y=1$, determine minimal and maximal value of $$A=x\sqrt{1+y}+y\sqrt{1+x}$$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013
Tags: inequalities, minimum, maximum
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2013
Tags: inequalities, minimum, maximum
If $x$ and $y$ are nonnegative real numbers such that $x+y=1$, determine minimal and maximal value of $$A=x\sqrt{1+y}+y\sqrt{1+x}$$