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在几何问题中,当某几何元素在给定条件变化时,求某几何量的最大值或最小值问题,被称为最值问题.确定几何图形中有关线段长度、周长、面积等最值问题是考试中常出现的题型.探求最值问题的方法一般有两种:(1)几何法:从运动中观察变化规律,运用几何中的不等量性质、定理;(2)代数法:揭示问题中变化元素的代数关系,通过构造一元二次方程或二次函数等代数方法求解.现举例说明.
In geometric problems, when a geometric element changes in a given condition, the problem of finding the maximum value or the minimum value of a geometric quantity is called the most value problem, and the most relevant value in the geometric figure about the length, circumference and area of the line The problem is the type of questions that often appear in the exam.Generally, there are two ways to explore the most value problem: (1) Geometry: Observe the law of change from the motion and use the inequality of geometry, theorem; (2) Algebraic method: Reveal the algebraic relationship among the changing elements in the problem, and solve the problem by constructing algebraic methods such as quadratic equations or quadratic functions.