It is not difficult to examine the knowledge points in mathematics test questions, but it must be considered from the opposite direction when solving problems (called "reverse thinking"), and students must pay attention to cultivating this useful ability.

Example of inverse problem of mathematical concept 1

If the result of simplifying 1-x is 2x-5, find the range analysis of x: the original formula = 1-x-x-4. It should be changed to: x- 1-(4-x)=2x-5. Considering from the opposite direction of the concept of absolute value, it is deduced that its conditions are 1-x≤0 and x-4 ≤ 0 ∴.

There are four rational numbers: 3,4-6, 10. These four numbers are added, subtracted, multiplied and divided (each number is used only once) to get the result of 24. Please write the formula that meets the requirements. Analysis: Imagine 3×8=24, and then consider how to calculate 8 from 4, -6, 10, so as to find the required formula 3 (4-6+10) = 24,4-(-6×10) ÷. 10-(-6×3+4); 3( 10-4)-(-6) and so on. Third, the reverse application of the nature of inequality Example 3

If the solution set of inequality (a- 1) x > a2-2 about x is x < 2, find the value analysis of a: according to inequality property 3, from the opposite direction, we find that A- 1 < 0, a2-2 = 2 (a-1) ∴ a. Fourth, the reverse analysis of fractional equation test example 4

Given that the equation -= 1 has an increasing root, find its increasing root. Analysis: The root of this fractional equation may be x= 1 or x=- 1. The denominator of the original equation is sorted, x2+mx+m- 1=0. If you substitute x= 1, you can get m = 3. If x=- 1 is substituted, m cannot be found; The value of ∴m is 3 and the root of the original equation is x= 1. V. Inverse Problem of Graphic Transformation Example 5

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