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解分母部分含有根式的无理方程,通常的方法是化无理为有理,化分式为整式,但有时运算量较大,笔者结合自己的教学实践,归纳了这类无理方程解法的一些方法和技巧。一利用函数的定义域和值域 [例1] 解方程 1/((x~2)+5x-14-1)~(1/2)-1/(2-(x+7)~(1/2)=((2-x+5)~(1/2)))/(5~(1/2))-1/(5~(1/2))分析,观察三个根式内部的关系:x~2+5x-14=(x+7)(x-2),试着先讨论末知数x的取值范围。
The denominator part contains a rootless irrational equation. The usual method is irrational and rational, and the fractional formula is integral. However, sometimes the amount of calculation is large. The author combined his own teaching practice to sum up some methods and techniques for solving such irrational equations. . A function using the definition of the domain and value range [Example 1] solution of the equation 1 / ((x ~ 2) + 5x-14-1) ~ (1/2) -1 / (2-(x + 7) ~ (1 /2)=((2-x+5)~(1/2)))/(5~(1/2))-1/(5~(1/2)) analysis, observe three internal Relationship: x~2+5x-14=(x+7)(x-2), try to discuss the range of the unknown number x.