当题目中的未知数具有对称关系时,应用基本对称式x+y=a,xy=b进行代换,可使解题过程简化。现以部分试题为例,介绍这种解题技巧在分式求值中的妙用。例1若x-1x=1,则x3-1x3=的值为()(A)3(B)4(C)5(D)6解:设1x=y,则x-y=1,xy=1。故x3-1x3=x3-y3=(x-y)3+3xy(x-y)=13+3×1=4。故选(B)。 When the unknowns in the title have a symmetric relationship, the application of the basic symmetry formula x+y=a, xy=b can simplify the problem-solving process. Take some test questions as an example to introduce the magical skills of this problem solving technique in the evaluation of fractions. Example 1 If x-1x = 1, then the value of x3-1x3 = () (A) 3 (B) 4 (C) 5 (D) 6 Solution: Let 1x = y, then xy = 1, xy = 1 . Therefore, x3-1x3=x3-y3=(x-y)3+3xy(x-y)=13+3x1=4. So choose (B).