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本文旨在探讨不等式中一类常见、重要的不等式:(x_1+x_2+…x_n)(1/x_1+1/x_2+…1/x_n)≥n~2并通过例题,说明利用这个不等式求解含有分式的不等式有关的问题的求解,不仅有章可循,而且比用其它方法求解更为简洁.命题:设x_1,x_2, …,x_n是n个正实数,(?)∈N且n≥2测(x_1+x_2_…x_n)(1/x_1+1/x_2+…1/x_n)≥n~2当且仅当x_1=x_2=…=x_n时等号成立,这个不等式就是本文所要介绍的倒数关系不等式.
The purpose of this paper is to investigate a common and important inequality in inequality: (x_1+x_2+...x_n)(1/x_1+1/x_2+...1/x_n)≥n~2 and passing examples to illustrate the use of this inequality to solve fractional inequalities The solution to the problems related to inequalities is not only rule-based, but also more concise than using other methods. Proposition: Let x_1, x_2, ..., x_n be n positive real numbers, (?) ∈ N and n ≥ 2 (x_1+x_2_...x_n)(1/x_1+1/x_2+...1/x_n)≥n~2 The equality holds if and only if x_1=x_2=...=x_n. This inequality is the reciprocal relational inequality to be introduced in this paper. .