在将无理方程或指数方程转化为一元二次方程时,会经常使用“根为正”与“有正根”用以过渡,有些粗心的同学将其混用,但二者之间确有着明显的界限,且看几例. [例1]若方程(1gax)(lagx2)=4的所有解都大于1,求a的取值范围. 解原方程可化为x>0a>0 21g2x+31galgx+1g2a-4=0 21g。 若令t=lgx,则①化为 t2+31gat+1g2a-4=0 ② 分析 若原方程的所有解都大于1,则lgx When converting an irrational equation or an exponential equation into a quadratic quadratic equation, the “root positive” and “positive root” transitions are often used, and some careless classmates mix them, but between the two. There are obvious boundaries, and see a few examples. [Example 1] If all solutions of the equation (1gax) (lagx2) = 4 are greater than 1, find the range of a. The original equation can be solved as x>0a>0 21g2x+31galgx+1g2a-4=0 21 g. If t = lgx, then 1 is converted to t2+31gat+1g2a-4=0 2 If all solutions of the original equation are greater than 1, then lgx