Question

已知m^2-5m+1=0,求m^3+1/m^3 和m-1/m的值

跪求

Answer 1

将m^2-3m-1=0两边同时除以m,得，
m-3-1/m=0,
整理：m-1/m=3
将m-1/m=3两边平方，得，
(m-1/m)²=9，
m^2-2+1/m^2=9,
即m^2+1/m^2=7
将m^2+1/m^2=7两边平方，得，
m^4+2+1/m^4=49
即m^4+1/m^4=47
m^3-1/m^3
=（m-1/m）(m^2+1+1/m^2)
=3×(7+1)
=24

Answer 2

m²-5m+1=0
m²+1=5m,方程式两边同时除以m，得到
m+1/m=5
（m+1/m）^3=m^3+1/m^3+3(m+1/m),所以
m^3+1/m^3=(m+1/m)^3-3(m+1/m)=5^3-3×5=110
(m+1/m)^2=m^2+1/m^2+2,
所以，m^2+1/m^2=(m+1/m)^2-2=5^2-2=23
(m-1/m)^2=m^2+1/m^2-2=23-2=21,
m-1/m=±√21
望采纳，多谢！