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一元二次方程ax~2+bx+c=0(a≠0)的两根为x_1,x_2,则由韦达定理知x_1+x_2=-b/a,x_1·x_2=c/a,可见定理反映了根与系数的关系。其形式简单,却包含了丰富的数学内容,应用广泛,具体表现在:应用韦达定理,求方程中参数的范围,求代数式的值;利用韦达定理逆定理,构造一元二次方程辅助解题。下面就以具体例题发现韦达定理的妙用之处。1活用韦达定理,求代数值例1.已知α,β是方程x~2-x-1=0的两个实数根,则代数式α~2+α(β~2-2)的值为()。
The two quadratic equations ax ~ 2 + bx + c = 0 (a ≠ 0) for the two x_1, x_2 by Vinda theorem know x_1 + x_2 = -b / a, x_1 · x_2 = c / a can be seen Theorem reflects the relationship between root and coefficient. Its form is simple, but contains a wealth of mathematical content, widely used, in particular: the application of Vedic theorem, find the range of parameters in the equation, and algebraic value; the inverse of the Veda theorem, constructs the quadratic equation auxiliary solution question. The following specific examples to discover the magical effect of the Vedic theorem. 1 Applying the Vedic theorem, find the algebraic example 1. Given that α and β are two real roots of the equation x ~ 2-x-1 = 0, the value of the algebraic α ~ 2 + α (β ~ 2-2) for().