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构造法就是根据某种需要,把题设条件或求解结论设想在某个模型上,通过对新设想模型的研究推出结论的解题思维方法.构造法解题能够打破常规、另辟蹊径,获得简捷、明快、精巧的解答.它是一种很重要的数学方法,其应用范围很广.加强这种训练,可以培养我们的创造思维能力和数学转化思想.下面举例说明. 一、构造函数 例 1 设f(x)=x4+ ax3+bx2+cx+d,其中 a、b、c、d为常数,若f(1)=1,f(2)=2,f(3)=3,则(f(4)+f(0))/4的值为 (A)1(B)4(C)7(D)8
The construction method is based on a certain need, conceives the conditions of the questions or solution conclusions on a certain model, and then puts forward a conclusion on the problem-solving thinking method through the research on the newly-conceived model. The constructive problem-solving problem can break the convention, create a new path, and obtain simple, A clear and elegant solution. It is a very important mathematical method, and its application is very wide. To strengthen this training, we can cultivate our creative thinking ability and mathematical transformation of ideas. The following examples illustrate. First, the constructor function Example 1 f (x) = x4 + ax3 + bx2 + cx + d, where a, b, c, d are constants, if f (1) = 1, f (2) = 2, f (3) = 3, then (f (4) The value of +f(0)/4 is (A)1(B)4(C)7(D)8