韦达定理的问题

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2025-04-09 13:57:40
推荐回答(1个)
回答1:

你问:韦达定理的问题;1、应该说你在运用方程ax²+bx+c=0
(a≠0)的两根是x1、x2,则:
x1+x2=-b/a
x1x2=c/a
2、由韦达定理
x1+x2=-1
x1x2=a
x11
则x1-10
所以(x1-1)(x2-1)<0
x1x2-(x1+x2)+1<0
a-(-1)+1<0
a=0)的方程用直接开平方求出方程的解为x=m+√n或是x=m-√n,这种解一元二次方程的方法就是直接开平方法。
通过观察不难发现第(1)、(2)两小题中的方程显然用直接开平方法好做;
(3)题因方程左边可变为完全平方式,右边的121>0,所以此方程也可用直接开平方法解;第(4)小题,方程左边可利用平方差公式,然后把常数移到右边,即可利用直接开平方法进行解答。

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