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西南师范大学出版社出版的初中数学试验教材(内地版)代版第二册P、136、1(3)题和实验课本高层次代数第2册P、108、3题都是关于x的方程:x+1/x=a+1/a,这个题目非常好。好在它的构造是倒数型、对称型,所以形式简洁美丽,好在它的解也对称、简明、易记,更好在能推广灵活运用也同样有对称美、简洁美。命题一方程:x+1/x=c+1/c(?)x_1=c,x_2=1/c(证略) 如果将未知数x换为x的函数f(x),则有: 命题二方程f(x)+1(f(x))=c+1/c(?)f(x)=c,f(x)=1/c,(其中x为未知数,f(x)为x的函数) 证明:∵f(x)≠0,c≠0。
The mathematics experiment textbook of junior high school published by Southwest Normal University Press (Mainland Edition) The second edition of P, 136, 1 (3) and the experimental textbook High Algebra The second volume of P, 108, and 3 questions are all about the equation of x :x+1/x=a+1/a, this topic is very good. Fortunately, its structure is reciprocal, symmetrical, so the form is simple and beautiful, but fortunately its solution is also symmetrical, concise, easy to remember, better to promote the use of flexibility also has the beauty of symmetry, simple beauty. Propositional equation: x+1/x=c+1/c(?)x_1=c, x_2=1/c (proof) If we change the unknown x to the function f(x) of x, we have: Proposition 2 The equation f(x)+1(f(x))=c+1/c(?)f(x)=c,f(x)=1/c, (where x is an unknown number and f(x) is an x The function) proves that ∵f(x)≠0, c≠0.