Question

1、已知x1,x2是方程x^2+mx+m-1=0的两个实数根,且x1^2+x2^2=17,求m的值

Answer 1

1题x1+x2=-m

x1x2=-1

则x1^2+x2^2

=(x1+x2)^2-2x1x2

=m^2+2=17

m=±√15

判别式大于等于0

m^2-4(m-1)>=0

(m-2)^2>=0

恒成立

所以m=±√15