已知m2-5m-1=0,求2m2-m+1/m2的值
问题描述:
已知m2-5m-1=0,求2m2-m+1/m2的值
答
感觉题目有错!请仔细检查!!
答
m^2-5m-1=0
m≠0,两边同除以m,得
m-1/m=5
(m-1/m)²=25
m²+1/m²-2=25
m²+1/m²=27
m^2-5m=1
2m^2-5m+(1/m^2)
=m²+m²-2m+(1/m²)
=m²+(1/m²)+1
=27+1
=28