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不等式的内容贯穿于整个高中数学之中,作为一种基本工具,不等式在高中数学领域中都有应用。诸如集合问题、方程组解的讨论、函数的定义域和值域的确定、三角、数列、复数、立体几何中的最值问题,都与不等式有着密切的联系。然而,不等式的应用主要可以分成两类:一类是应用几何平均数和算术平均数定理求最值;另一类是解不等式和证明不等式在其他数学问题中应用。
The content of inequalities runs through the entire high school mathematics. As an essential tool, inequalities have applications in the field of high school mathematics. Problems such as set problems, the discussion of equation sets, the definition of function domains, and the determination of value domains, and the most value problems in trigonometry, sequence, complex numbers, and solid geometry all have close links with inequalities. However, the application of inequality can be mainly divided into two categories: one is to apply geometric mean and arithmetic mean theorem to find the best value; the other is to apply inequality and prove inequality in other mathematical problems.