Question

a的a次方b的b次方与a的b次方b的a次方谁大?a＞b＞0.

Answer 1

a^a*b^b/a^b*b^a

=a^(a-b)*b^(b-a)

=a^(a-b)*(1/b)^(a-b)

=(a/b)^(a-b)

a＞b＞0

a/b>1

a-b>0

原式=(a/b)^(a-b)>1^0=1

a^a*b^b/a^b*b^a>1

a^a*b^b>a^b*b^a