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在解决数学问题时,如果能将数量关系与几何图形的性质结合起来进行分析,并通过数的运算去寻找图形之间的联系,同时结合题中所给的已知条件去构造图形,或结合已知图形去寻找数量之间的关系．这样不但可以使复杂问题简单化,而且有利于拓宽解题思路．这种解决问题的思想即为“数形结合”思想．例已知a、b都是小于1的正数,求证：a~2+b~2~(1/2)+(1-a)~+b~2~(1/2)+ a~2+(1-b)~2~(1/2)+(1-a)~2+(1-b)~2~(1/2)≥2~(1/2)．分析：对形如a~2+b~2~(1/2)的问题,不妨考虑利用勾股定理和题中所给
When solving mathematical problems, if we can combine quantitative relations with the nature of geometrical figures for analysis, and through the number of operations to find the connection between graphics, combined with known conditions given in the question to construct graphics, or combine Known graphs to find the relationship between numbers. This will not only simplify the complexity of the problem, but also help broaden the problem-solving ideas. The idea of solving this problem is the idea of “combination of numbers and forms”. For example, it is known that both a and b are positive numbers that are less than one. Prove that: a~2+b~2~(1/2)+(1-a)~+b~2~(1/2)+ a~2 +(1-b)~2~(1/2)+(1-a)~2+(1-b)~2~(1/2)≥2~(1/2). Analysis: For questions such as a~2+b~2~(1/2), consider using the Pythagorean theorem and the questions given in the question