Problem
ALG-B1-M07-P004 Largest product
#4
★☆☆☆☆ Level 1 of 5
Let \(x,y>0\) and \(x+y=10\). Prove that \(xy\le25\).
Apply AM-GM to \(x\) and \(y\).
\(\frac{x+y}{2}\ge\sqrt{xy}\), so \(5\ge\sqrt{xy}\). Hence \(xy\le25\). Equality occurs when \(x=y=5\).
A first problem on fixed sum and maximum product.