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挖掘和利用。隐含条件,通常是从数学题所涉及的概念、图形、数量、结构等方面的特征入手,通过分析、比较、观察、联想等方法,以便使条件明朗化、完备化和具体化。一、根据概念特征挖掘隐含条件有些数学题,可以从分析概念的本质特征入手,挖掘隐含条件,发现解题契机。例1 方程|x-1992|+(1992-59x)~(1/2)=1992的实数根是____。(第五届初中《祖冲之杯》数学邀请赛试题) 分析:由算术根定义可知,所给的隐含条件是1992-59x≥0,故|x-1992|1992-x,从而原方程化为:(1992-59x)~(1/2)=x,解得x_1=24,x_2=-83(增根)。例2 已知1/a~2+1/a-1=0,b~4+b~2-1=0,且1/a≠b~2,求ab~2+1/a的值。(1986年湖北黄冈数学竞赛题)
Tap and use. Implicit conditions usually begin with the features, concepts, figures, quantities, and structures involved in mathematics problems. Through analysis, comparison, observation, association, and other methods, conditions are made clear, complete, and concrete. First, mining hidden conditions based on the concept of features Some math problems, you can start with the analysis of the essential characteristics of the concept, mining hidden conditions, find the opportunity to solve problems. Example 1 The real root of the equation |x-1992|+(1992-59x)~(1/2)=1992 is ____. (The fifth junior high school “Zu Chong Cup” mathematics invitational exam questions) Analysis: From the definition of the arithmetic root, we can see that the implicit condition given is 1992-59x ≥ 0, so |x-1992|1992-x, and thus the original equation is: (1992-59x) ~ (1/2) = x, solution x_1 = 24, x_2 = -83 (increase root). Example 2 It is known that 1/a~2+1/a-1=0, b~4+b~2-1=0, and 1/a≠b~2, find the value of ab~2+1/a. (1986 Hubei Huanggang Mathematics Competition)