Question

已知a>b>0,则a2+1/ab+1/a（a-b）的取值范围是?

Answer 1

因为a^2=a^2-ab+ab=a(a-b)+ab,

所以a^2+1/ab+1/a(a-b)

=ab+1/ab+a(a-b)+1/a(a-b)

≥2+2=4,

所以a^2+1/ab+1/a（a-b）的取值范围是[4,+∞)