Question 5
Let $a,b,c$ be positive real numbers. Prove that
$$\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2}\le8.$$
Proposed by Zuming Feng and Titu Andreescu (as credited in the supplied source).
$$\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2}\le8.$$
Proposed by Zuming Feng and Titu Andreescu (as credited in the supplied source).