本刊今年第6期《从方程x+1/x=c+1/c的解法谈起》一文中,将初中《代数》课本第三册中的一道练习题“解关于x的方程x+1/x=c+1/c”作了两次推广: 推广一:关于x的方程x+b/x=c+b/c的解为x_1=c,x_2=b/c(c≠0)。 推广二:关于x的方程x~(1/n)+1/(x~(1/n))=c+1/c的解为x_1=c~n,x_2:=1/(c~n)。 In the 6th issue of this year’s book “On the solution to the equation x+1/x=c+1/c”, we will solve one equation in the third volume of the “Algebra” textbook for junior high school. 1/x=c+1/c” is generalized twice: Generalization 1: The solution to the equation x+b/x=c+b/c for x is x_1=c, x_2=b/c(c≠0 ). Generalization 2: The solution of the equation x~(1/n)+1/(x~(1/n))=c+1/c for x is x_1=c~n, x_2:=1/(c~n ).