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隐含条件指的是隐蔽在题设内的不易被察觉的条件,它在很多数学问题的解题过程中往往显示着不可低估的特殊作用.笔者以近几年的中考题为例介绍几种常见的功能,供同学们学习时参考. 一、导向功能 隐含条件对许多问题的求解有着明显的导向作用,先考虑隐含条件,有助于合理地选择思维方法,更加明确思维目标. 例1 实数p、q满足p2-2p-5=0,5q2+2q-1=0,求p2+1/q2的值. 分析乍看起来解此题似乎难以下笔,但注意到已知两等式中隐含着极重要的信息.当p≠1/q时,p,1/q是关于x的方程为x2-2x-5=0两实根.由根与系数的关系可得 p+1/q=2,p·1/q=-5, ∴ p2+1/q2=(p+1/q)2-2·p/q=14.
Implicit condition refers to the conditions that are not easily perceived in hidden questions. It often shows a special role that cannot be underestimated in the process of solving problems in many mathematics problems. The author takes the middle exam questions in recent years as an example to introduce several common problems. The function is for reference when students learn. First, the implicit function of guidance function has a clear guiding role in the solution of many problems. First consider the implicit conditions, help to rationally choose the way of thinking, and more clearly the target of thinking. Example 1 The real numbers p, q satisfy p2-2p-5 = 0, 5q2 + 2q-1 = 0, find the value of p2+1/q2. Analysis seems to be difficult to write the solution to this problem, but notice the known two equations Implicitly important information is implied. When p ≠ 1/q, p, 1/q is an equation about x that is x2-2x-5 = 0, two real roots. The relationship between the root and the coefficients yields p+1/ q=2,p·1/q=-5, ∴ p2+1/q2=(p+1/q)2-2·p/q=14.