同学们解无理方程时常会遇到这样的情况:将方程进行变形,把其中的根号“化去”,变成整式方程时,发现这个整式方程无实数根;或者虽有实数根,经检验知它的根不是原方程的根.这两种情形都得出原方程无解的结论.至此,我们解这个无理方程的任务完成了.但我们总有那么一点遗憾,好像自己白忙了一阵子,甚至有一种受骗的感觉.如果我们不这么“按部就班”地解这类无理方程,而是通过别的途径,直接“判断”其无解,就用不着“白忙一阵子”了. Students often solve the unreasonable equations when they encounter such a situation: When the equations are transformed, and the root numbers are “transformed” into integral equations, the whole equations are found to have no real number roots; or if there are real roots, they are tested. Knowing that its root is not the root of the original equation. Both of these situations lead to the conclusion that the original equation has no solution. At this point, we have completed the task of solving the irrational equation. But we always have a little regret, as if we are busy There was even a feeling of being deceived. If we do not “step” to solve this kind of unreasonable equation, but instead “judge” it without solution by other means, we don’t need to “white for a while”.