Problem
ALG-B1-M10-P005 Estimate with a reciprocal
#5
★☆☆☆☆ Level 1 of 5
For \(x>0\), prove that \(x+\frac{4}{x}\ge4\).
Apply AM-GM to \(x\) and \(\frac{4}{x}\).
\(x+\frac{4}{x}\ge2\sqrt{x\cdot\frac{4}{x}}=4\). Equality occurs at \(x=2\).
AM-GM is not announced; the student should recognize it.