解
應(yīng)該缺了正數(shù)的條件,x+1>0,y>0
2x+y=2
2(x+1)+y=4
2/(x+1)+1/y
=4/[2(x+1)]+4/(4y)
=[2(x+1)+y]/[2(x+1)]+[2(x+1)+y]/(4y)
=1+y/(2x+2)+(2x+2)/4y+1/4
=5/4+y/(2x+2)+(2x+2)/(4y)
≥5/4+2√(1/4)
=5/4+1
=9/4
當(dāng)且僅當(dāng) y/(2x+2)=(2x+2)/4y
即x=1/3,y=4/3時(shí)等號(hào)成立
所以,所求最小值為9/4