Problem
ALG-B1-M07-P002 Minimum of x + 1/x
#2
★☆☆☆☆ Level 1 of 5
For \(x>0\), find the least value of \(x+\frac{1}{x}\).
Apply AM-GM to \(x\) and \(\frac{1}{x}\).
By AM-GM, \(x+\frac{1}{x}\ge2\sqrt{x\cdot\frac{1}{x}}=2\). Equality holds at \(x=1\), so the minimum is \(2\).
Check the condition \(x>0\): without it AM-GM cannot be applied.