1/a+9/b =( 1/a+9/b)* 1 =( 1/a+9/b)*(a+b)= 1+b/a+9a/b+9 & gt； = 10+2 gen Hao 9 = 10+2 * 3 = 16

So the minimum value is 16.

According to the basic conditions of basic inequality, the equal sign holds if and only if b/a = 9a/b.

A+b= 1, so a= 1/4 b=3/4 (required).

Conversely, when a= 1/4 b=3/4, 1/a+9/b= 16 (enough).

good