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在数学中,化归不仅是思考问题与解决问题的指导思想,而且众多的数学方法也隶属于化归思想的范畴,所以化归也是一种具体的方法和手段、许多重要的数学思想和研究策略都可以用化归思想的精髓——矛盾转化来概括,如代数中多元到一元;高次到低次;几何中空间到平面,高维到低维,曲线到直线;分析中无限到有限,多元积分到一元积分等等.解决数学问题常常离不开化归法. 例 1 设 a,b,A,B为已知实数,函数f(x)=1—acosx-bsinx-Acos2x-Bsin2x,求证若对一切实数x,有f(x)≥0,则a2+b2≤2,A2+B2≤1.
In mathematics, transformation is not only the guiding ideology of problem solving and problem solving, but also a large number of mathematical methods belong to the category of transformation. Therefore, transformation is also a specific method and method, many important mathematical ideas and research. Strategies can be summed up with the paradoxical transformation of ideas, such as multivariate to unity in algebra; from high to low; from geometry to plane in geometry, from high dimension to low dimension, from curve to straight line; from infinite to finite in analysis. , Multivariate integral to one dollar integral and so on. Solving mathematical problems can not be separated from normalization. Example 1 Let a, b, A, B be known real numbers, function f(x)=1—acosx-bsinx-Acos2x-Bsin2x, Verify that if all real numbers x have f(x) ≥ 0, then a2+b2≤2, A2+B2≤1.