Problem 935 (difficulty: 3/10)

Let \(\displaystyle p,q>0\) and \(\displaystyle 1/p+1/q=1\). Show that for all \(\displaystyle x,y\geq 0\)

\(\displaystyle xy\leq {x^p \over p} + {y^q \over q}.\)

Give me another random problem!