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在解有关一元二次方程的根的问题时,同学们习惯于用韦达定理求解.其实,有时直接求出方程的根,更能迅速地解决问题.现举例说明. 例1已知关于x的方程x~2-2mx+m~2-1=0的两个实根x_1、x_2满足x_1~2+x_2~2=4,求m的值. 分析:因为x~2-2mx+m~2-1可分解为(x-m+1)(x-m-1),所以易求得方程的根为:x_1=m-1,x_2=m+1.根据x_1~2+x_2~2=4,可列出m满足的方程,进
When solving the problem concerning the root of the one-dimensional quadratic equation, students are accustomed to solving using Vedic theorem. In fact, sometimes the root of the equation is directly solved and the problem can be resolved more quickly. Now an example is shown. Example 1 is known about x The two real roots x_1, x_2 of the equation x~2-2mx+m~2-1=0 satisfy x_1~2+x_2~2=4, find the value of m. Analysis: Since x~2-2mx+m~ 2-1 can be decomposed into (x-m+1)(xm-1), so the root of the easy equation is: x_1=m-1, x_2=m+1. According to x_1~2+x_2~2=4 , can list equations satisfied by m, into