论文部分内容阅读
两点间的距离公式是解析几何中的重要公式之一,它的应用极为广泛。本文举数例说明两点间距离公式在代数不等式的证明和求最火值、最小值中的应用。一证明代数不等式例1 设a_1、a_2、b_1、b_2均为实数。求证 ((a_2-a_1)~2+(b_2-b_1)~2)~(1/2) ≤(a_1~2+b_1~2)~(1/2)+(a_2~2+b_2~2)~(1/2)。分析此不等式的左边可看作是坐标平面内两点(a_1,b_1)、(a_2,b_2)之间的距离;不等式右边可看作是点(a_1,b_1)、(a_2,b_2)到原点的距离之和。由此,不难想到:是否可应用两点间距离公式来证明。证明设A(a_1,b_1)、B(a_2,b_3)是坐
The distance formula between two points is one of the important formulas in analytical geometry, and its application is extremely extensive. In this paper, several examples are given to illustrate the application of the distance formula between two points in the proof of algebraic inequality and the search for the maximum fire value and minimum value. A proof algebraic inequality Example 1 Let a_1, a_2, b_1, and b_2 be real numbers. Proof ((a_2-a_1)~2+(b_2-b_1)~2)~(1/2) ≤(a_1~2+b_1~2)~(1/2)+(a_2~2+b_2~2) ~(1/2). The left side of the analysis of this inequality can be seen as the distance between two points (a_1, b_1), (a_2, b_2) in the coordinate plane; the right side of the inequality can be seen as the point (a_1, b_1), (a_2, b_2) to the origin The sum of distances. From this, it is not difficult to think: whether the two-point distance formula can be used to prove. Prove that A(a_1,b_1) and B(a_2,b_3) are sitting