Question

若x，y是正數，則(x+

1

2y

)2+(y+

1

2x

)2的最小值是______．

Answer 1

(x+

1

2y

)2+(y+

1

2x

)2≥2(x+

1

2y

) (y+

1

2x

) =2（xy+

1

4xy

+1）≥2（2×

xy

×

1

4xy

+1）=4
故答案為4