题目

已知方程3x²-4x=-1的两根是x1 x2,不解方程,求：1.x2/x1 + x1/x2 2.（x1 - 2）（x2 - 2）

提问时间：2021-01-02

答案

方程3x²-4x=-1可化为：3x²-4x+1=0
由根与系数的关系,有
x1+x2=4/3, x1x2=1/3
∴x2/x1 + x1/x2
=(x1²+x2²)/(x1x2)
=[(x1+x2)²－2x1x2]/(x1x2)
=[(4/3)²－2×(1/3)]/(1/3)
=[(16/9)-(2/3)]/(1/3)
=(10/9)／(1/3)
=10/3

(x1-2)(x2-2)
=x1x2-2x1-2x2+4
=x1x2-2(x1+x2)+4
=(1/3)-2×(4/3)+4
=(1/3)-(8/3)+4
=(-7/3)+4
=5/3.