某些代数题借助几何方法来解,可以加强直观形象,有时甚至是很巧妙的.例如下面的这些问题,一些书刊中常把它作为用几何方法来解代数问题的范例: 例1:设两正变量x、y,满足方程x+y=c,试证函数z=(x~2+a~2)~(1/2)+(y~2+b~2)~(1/2)的最小值为(c~2+(a+b)~2)~(1/2),其中a、b、c是给定的正数。 Some algebraic problems are solved by geometric methods, which can enhance the intuitive image, sometimes even clever. Such as the following problems, some books and magazines often use it as a geometric method to solve the problem of algebraic examples: Example 1: Set two positive The variables x and y satisfy the equation x+y=c and the trial function z=(x~2+a~2)~(1/2)+(y~2+b~2)~(1/2) The minimum value is (c~2+(a+b)~2)~(1/2), where a, b, and c are given positive numbers.