Question

（j00j•福建）已知非負(fù)實(shí)數(shù)x，y滿足

1

x

+

4

y

=1，則非負(fù)實(shí)數(shù)x+y滿足的最大值為______．

Answer 1

∵非負(fù)實(shí)數(shù)x，y滿足

1

x

+

4

y

=1，
∴非負(fù)實(shí)數(shù)x+y=（x+y）(

1

x

+

4

y

)=0+

y

x

+

4x

y

≥0+2

4x y • y x

=9．
∴非負(fù)實(shí)數(shù)x+y滿足的最大值為9．