有条件限制的双变元取值问题,涉及领域宽,知识面广,需要善于转化,可以通过消元转化为函数求值域问题,但是当题目具有一定特殊形式对,也可通过另外两种常用方法转化.一、消元变函数例1 已知3x~2+2y~2=6x,求 u=x~2+y~2的取值范围.分析:为了求出 u 的范围,需将变量 x,y 用一个变量 x 表示出 u,此时要注意 x 的范围.解:由3x~2+2y~2=6x,得y~2=(1/2)(6x-3x~2)∵y~2≥0,∴x∈[0,2]u=x~2+y~2=x~2+(1/2)(6x-3x~2)=-(1/2)(x-3)~2+(9/2)结合二次函数的图象可知,u∈[0,4] The conditional limited double variable value problem, which involves a wide field, wide knowledge, needs good conversion, can be converted to a function evaluation domain problem through elimination, but when the problem has a certain special form, it can also pass the other two Commonly used methods for conversion. First, the metavariable function example 1 is known 3x~2+2y~2=6x, find u=x~2+y~2 range of values. Analysis: In order to find the scope of u, need to The variable x,y is denoted by a variable x, and attention must be paid to the range of x. Solution: From 3x~2+2y~2=6x, get y~2=(1/2)(6x-3x~2) ∵y~2≥0, ∴x∈[0,2]u=x~2+y~2=x~2+(1/2)(6x-3x~2)=-(1/2)(x -3)~2+(9/2) Combined quadratic function images show that u∈[0,4]