设m^2-3m+1=0,n^2-3n+1=0,且m≠n,求代数式1/m^2+1/n^2的值_数学解答

设m^2-3m+1=0,n^2-3n+1=0,且m≠n,求代数式1/m^2+1/n^2的值

人气：483 ℃　时间：2019-11-11 15:16:39

解答

m^2-3m+1=0,n^2-3n+1=0
m,n是方程x^2-3x+1=0的两根
m+n=3,mn=1
1/m^2+1/n^2=(m^2+n^2)/(mn)^2=[(m+n)^2-2mn]/(mn)^2
=(9-2)/1
=7