论文部分内容阅读
在某些数学问题中,如可由题设条件出发构造一元二次方程,往往能使解法简洁流畅,别具一格. 例l △ABC中,求证: cos2A十cos2B+cos2C+2cosAcosBcosC=1. 分析构造x的一元二次方程 x2+2cosBcosCx+(cos2B+cos2C-1)=0. (*) 只要证明x=cosA为方程(*)的一个根即可.
In some mathematics problems, if you construct a quadratic equation from the condition of the problem, you can often make the solution concise and fluent. In the case of △ABC, verify that: cos2A+cos2B+cos2C+2cosAcosBcosC=1. A unitary quadratic equation x2+2cosBcosCx+(cos2B+cos2C-1)=0. (*) As long as x=cosA is proved to be a root of equation (*).