已知一元二次方程x²-2x+m-1=0.设x1,x2是方程的两个实数根,且满足x1²+x1x2=1,求m的值提示:x²-(x1+x2)x+x1x2=0

问题描述:

已知一元二次方程x²-2x+m-1=0.设x1,x2是方程的两个实数根,且满足x1²+x1x2=1,求m的值
提示:x²-(x1+x2)x+x1x2=0

x1+x2=2
x1x2=m-1
x1²+x1x2
=x1(x1+x2)
=2x1=1
x1=1/2
x2=3/2
x1x2=m-1=3/4
m=7/4