∵(a+b)(1/a+2/b)=3+b/a+2a/b≥3+2√2 ,a+b=1∴1/a+2/b最小值为3+2√2
根据柯西不等式：(a+b)(1/a+2/b)≥(1+√2)²∴(1/a+2/b)≥(1+√2)²=3+2√2
