Problem
ALG-B2-M08-P001 One ratio
#1
★★☆☆☆ Level 2 of 5
Let \(a,b>0\). Prove \(\frac{a}{b}+\frac{b}{a}\ge2\), using the substitution \(x=a/b\).
Hint. After substitution, it remains to prove \(x+\frac1x\ge2\).
Set \(x=a/b\). Then \(b/a=1/x\), and \(x+\frac1x-2=\frac{(x-1)^2}{x}\ge0\).
Teaching goal: recognize the appropriate substitution and check the domain.