Question

设x大于0 y大于0且x+2y=1 求1÷x+1÷y最小值

Answer 1

∵x＞0,y＞0.且x+2y=1.∴由题设及基本不等式可知(1/x)+(1/y)=(x+2y)[(1/x)+(1/y)]=3+(x/y)+(2y/x)≥3+2√2.∴[(1/x)+(1/y)]min=3+2√2.