若正数x，y满足2x+3y=1，则1x+1y的最小值为5+265+26．

Question

若正数x，y满足2x+3y=1，则(1)/(x)+(1)/(y)的最小值为

5+2√(6)

5+2√(6)

．

Answer 1

∵正数x，y满足2x+3y=1，
∴(1)/(x)+(1)/(y)=（2x+3y）((1)/(x)+(1)/(y))=5+(3y)/(x)+(2x)/(y)≥5+2√((3y)/(x)•(2x)/(y))=5+2√(6)，当且仅当2x＝√(6)y=√(6)-2时取等号．
故答案为：5+2√(6)．