Question

若a,b为正实数,且a不等于b,比较(a^3)/(b^2)+(b^3)/(a^2)与a+b大小.十万火急!有分!

Answer 1

(a^3)/b^2+(b^3)/a^2-a-b

=(a^5+b^5-a^3b^2-b^3a^2)/(ab)^2

=[(a^2-b^2)a^3-(a^2-b^2)b^3]/(ab)^2

=(a^2-b^2)(a^3-b^3)/(ab)^2>0

(a^3)/(b^2)+(b^3)/(a^2)>a+