一个新不等式公式的证明与应用

Proof and Application of a New Inequality Formula

无论在初等数学还是在高等数学中,不等式都是十分重要的内容,而不等式的证明是不等式知识的重要组成部分,在该文中发现了分式不等式证明的新公式,利用新公式:a_(1)^(3)/b_(1)+a_(2)^(3)/b_(2)+…a_(n)^(3)/b_(n)≥(a_(1)^(2)+a_(2)^(2)+…+a_(n)^(2))(a_(1)+a_(2)+…+a_(n))/(b_(1)+b_(2)+…+b_(n)(其中a_(i),b_(i)∈R^(+),{a_(i)},{b_(i)}反序,i=1,2,…,n),巧证一类分式不等式,从而使分式不等式的证明方法更加完善,有利于进一步探讨和研究分式不等式的证明。

Inequality is a very important content in both elementary mathematics and advanced mathematics, and the proof of inequality is an important part of inequality knowledge. In this paper, a new formula for the proof of fractional inequality is found. Using the new formulae use new formula:a_(1)^(3)/b_(1)+a_(2)^(3)/b_(2)+…a_(n)^(3)/b_(n)≥(a_(1)^(2)+a_(2)^(2)+…+a_(n)^(2))(a_(1)+a_(2)+…+a_(n)/(b_(1)+b_(2)+…+b_(n)(a_(i),b_(i)∈R^(+),i=1,2,…,n),a class of fractional inequality is skillfully proved, which makes the proof method of fractional inequality more perfect and is conducive to further discussion and research on the proof of fractional inequality.