18. The inequality $x+2 \sqrt{2 x y} \leqslant a(x+y)$ holds for all positive numbers $x, y$. Then the minimum value of the real number $a$ is $\qquad$
18.2.

Since $x+2 \sqrt{2 x y} \leqslant x+(x+2 y)=2(x+y)$, then the minimum value of $a$ is 2.