阅读最近两年来全国各地的初中数学竞赛试题,有关“一元二次方程的根”的试题频频出现.这类试题不仅要运用一元二次方程根与系数的关系(即韦达定理)、根的判别式,而且往往要对所求(证明)的问题作恰当的代数式变换,其中既有数值的巧妙计算,同时又蕴含着巧妙的变换技巧与变换方法.现选取具有典型性的几例.解析其求解方法与技巧,领悟其隐含 Read the questions of junior high school mathematics contests across the country in the past two years. The questions about the “root of a quadratic equation” appear frequently. This kind of test should not only use the relationship between the root and the coefficient of a quadratic equation (ie, the Weddah’s theorem). The discriminant of the roots, and often the proper algebraic transformation of the problem sought (proved), in which there is a clever calculation of numerical values, but also contains ingenious transformation techniques and transformation methods. Now select a few typical cases. Analyze its solution methods and techniques to understand its implications