Question 172
Prove that the inequality
$$
x^2\sqrt{1+2y^2} + y^2\sqrt{1+2x^2} \ge xy(x+y+\sqrt{2})
$$
holds for any two real numbers $x$ and $y$.
$$
x^2\sqrt{1+2y^2} + y^2\sqrt{1+2x^2} \ge xy(x+y+\sqrt{2})
$$
holds for any two real numbers $x$ and $y$.