本文以較有系統的叙述,討論中學範圍內無理方程的解法,特別着重討論無理方程的增根及在實數範圍内無根(以後凡談到有根或無根均指在實數範圍內而言)的問題,給出若干規律以簡化驗根的手續。假若我們能用理論和實踐相結合的方法去指導學生,那末就可以逐漸培養他們的分析力、判斷力以及獨立思考的能力,從而减少激條式的驗根演算,改變學生們知其然而不知其所以然的不良學習方法。 This article uses a more systematic narrative to discuss the solution of irrational equations in secondary schools, with particular emphasis on discussing the rooting of irrational equations and the absence of roots in the real range (after all references to rooted or unrooted refer to the real number range). Problem, given a number of rules to simplify the procedure of root detection. If we can use a combination of theory and practice to guide students, then we can gradually develop their analytical power, judgment, and ability to think independently, so as to reduce the radical calculus calculus, change the students know it but I do not know Its bad learning method.