将a+2b=1代入欲求式,得：
1/a+1/b
=(a+2b)/a+(a+2b)/b
=(1+2b/a)+(a/b+2)
=a/b+2b/a+3
≥[2√(a/b×2b/a)]+3
=3+2√2
等号当且仅当a/b=2b/a,即a=√2-1,b=(2-√2)/2时成立.