设$\left\{p,q,r,s\right\}=\left\{a,b,c,d\right\},p\geq q\geq r\geq s$,由排序不等式,$\ a^2bc+b^2cd+c^2da+d^2ab=a(abc)+b(bcd)+c(cda)+d(dab)
\le p\left(pqr\right)+q\left(pqs\right)+r\left(prs\right)+s\left(qrs\right)=\left(pq+rs\right)\left(pr+qs\right)\le\left(\frac{pq+rs+pr+qs}{2}\right)^2=\frac{1}{4}(\left(p+s\right)\left(q+r\right))^2\le\frac{1}{4}\left(\left(\frac{p+q+r+s}{2}\right)^2\right)^2=4.$
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发表于 2020-11-21 22:17
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