一个不等式的证明及其应用

Some Applications of an Inequality and Its Proof

运用实对称矩阵的特征值理论及三次方程著名的Ｃａｒｄａｎｏ公式导出一类有趣的不等式，并给出几个重要特例．例举在常微分方程和分析学中的若干应用．

An interesting inequality is found in the eigenvalue theory of symmetrical real matrix as well as the famous Cardano's formula.A few important cases such as some classical inequalities in our result are shown.Some applications to two branches (ordinary differential equations and functional analysis) are given.