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方程根的定义,如果x=a是方程的一个根,那么这个根可以代入原方程,这样能使解题步骤简化.1·如《中小学数学(初中版)》,2007年第12期30页中,如果已知α、β是方程x2+3x-1=0的两个实数根,那么α2+2α-β的值是多少?分析因为α、β是方程x2+3x-1=0的两个实数根,根据方程根的定义,所以α2+3α-1=0.再利用一元二次方程的根与系数的关系,α+β=-3,能求出α2+2α-β这个非对称式的值.正象邹振兴老师在文
The definition of the root of the equation, if x=a is a root of the equation, then the root can be substituted into the original equation, which can simplify the problem solving.1· For example, “Mathematics for Elementary and Junior High School”, No.12, 2007 On the page, if α and β are known as the two real number roots of the equation x2+3x-1=0, what is the value of α2+2α-β? Analysis Because α, β is the equation x2+3x-1=0 Two real roots, according to the definition of the root of the equation, so α2+3α-1=0. Reuse the relationship between the root and coefficient of the quadratic equation, α+β=-3, we can find the non-linear α2+2α-β. Symmetrical values, just like Zou Zhenxing’s teacher