若a、b是正数,则(3a+1/b)2+(3b+1/a)2的最小值为_.
问题描述:
若a、b是正数,则(3a+
)2+(3b+1 b
)2的最小值为______. 1 a
答
∵a,b是正数,∴(3a+1b)2+(3b+1a)2≥2(3a+1b)(3b+1a)=2(9ab+1ab)+12等号成立的条件是3a+1b=3b+1a解得a=b,①又(9ab+1ab)≥29ab×1ab= 6.等号成立的条件是9ab=1ab ②由①②联立解得x=y=33,即当...