Question

已知m^2+m-1=0，求m^2+1/m^2的值

要过程哦

Answer 1

m²+m-1=0
m²-1=m
两边平方
m^4-2m²+1=m²
m^4+1=3m²
两边除以m²
m²+1/m²=2

Answer 2

a/sinA=b/sinB=c/sinC=k
则sinA=a/k
其他同理，代入式子中，约去k
有c²-a²-b²+ab=0
a²+b²-c²=ab
所以cosC=(a²+b²-c²)/2ab=1/2
所以C=60度
设PQ是y=kx+b
1=-k+b
2=2k+b
所以k=1/3,b=4/3
所以y=x/3+4/3
代入x+my+m=0
x+mx/3+4m/3+m=0
(3+m)x=-7m
x=-7m/(3+m)

在线段PQ上则-1<=x<=2
即-1<=-7m/(3+m)<=2

-1<=-7m/(3+m)
7m/(3+m)-1=(6m-3)/(3+m)<=0
(2m-1)(m+3)<=0
-3<m<=1/2

-7m/(3+m)<=2
7m/(3+m)+2=(9m+6)/(3+m)>=0
(3m+2)(m+3)>=0
m<-3,m>=-2/3

所以-2/3<=m<=1/2
所以在延长线上则m<-2/3,m>1/2