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恩格斯曾将数学凝练地概括为:数学是研究空间形式与数量关系的学科.可见,在许多数学问题中,都会含有常量、参量、变量等多个量(统称为数量),有时按照常规思维对这些数量主次性的区分往往使我们陷入繁难甚至无法解决的境地,但若变换角度,反客为主,往往能事半功倍,收到意想不到的效果.例1(2012年江苏省预赛第11题)解关于x的方程(cos2θ/2)x3+(3cos2θ/2-4)x+sinθ=0.
Engels once summed up mathematics concisely as follows: Mathematics is a discipline that studies the relationship between the form and quantity of space, and shows that in many mathematical problems, there are many quantities (collectively, quantities) of constants, parameters and variables, sometimes according to conventional thinking The distinction between the primary and secondary of these quantities tends to make us into a difficult or unsolvable situation, but if we change perspectives and refuse to dominate, we often can do more with less, and we can expect unexpected results. Example 1 (Jiangsu Provincial Preliminary Round 11 Question 2012) The equation for x (cos2θ / 2) x3 + (3cos2θ / 2-4) x + sinθ = 0.