Problem
ALG-B2-M07-P006 One variable equals one
#6
★★★☆☆ Level 3 of 5
Prove for \(a,b>0\): \[\frac{a^2+b^2}{ab}\ge2.\]
Hint. The expression has degree \(0\). Set \(b=1\).
Let \(x=a/b\). The inequality becomes \(x+\frac1x\ge2\), which follows from \((x-1)^2\ge0\) after multiplying by \(x>0\).
Practice with degree-zero normalization.