:(am+bm)(bm+an)=abm^2+(a^2+b^2)mn+abn^2
=(a^2+b^2)mn+ab(m^2+n^2)
>=(a^2+b^2)mn+2abmn
=mn(a^2+2ab++b^2)
=mn(a+b)^2 a+b=1
=mn
所以
(am+bm)(bm+an)大于等于mn