设a,b属于R+,a不等于b,且a+b=1,则1/a+1/b的取值范围是?

Question

设a,b属于R+,a不等于b,且a+b=1,则1/a+1/b的取值范围是?

Answer 1

设a,b属于R+,a不等于b,且a+b=1,则1/a+1/b=（a+b)/a+(a+b)/b=1+b/a+a/b+1
=2+b/a+a/b>=2+2根号（a/b*b/a)=4,但是取等号的条件不能满足,
故1/a+1/b>4