设1/a+1/b=5/<a+b>,求a/b^2+b/a^2的值?

过程我要 一定要正确哦!~

1/a+1/b=(a+b)/ab=5/(a+b)

=>

5ab=(a+b)^2=a^2+2ab+b^2

=>

a^2+b^2=3ab

a/b^2+b/a^2=(a^3+b^3)/[(a^2)*(b^2)]

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

=(a+b)*2ab/[(a^2)*(b^2)]

=2(a+b)/ab

=10/(a+b)