若m+1/m=-2.求：1.m^4+1/m^4; 2.m^4-1/m^4。

1.m+1/m=-2
(m+1/m)^2=4
m^2+1/m^2+2m*(1/m)=4
m^2+1/m^2+2=4
m^2+1/m^2=2
(m^2+1/m^2)^2=4
m^4+1/m^4+2m^2*(1/m^2)=4
m^4+1/m^4+2=4
m^4+1/m^4=2

2.(m-1/m)^2
=m^2-2m*(1/m)+1/m^2
=m^2+1/m^2-2
=2-2
=0
m-1/m=0

m^4-1/m^4
=(m^2+1/m^2)(m^2-1/m^2)
=(m^2+1/m^2)(m+1/m)(m-1/m)
=(m^2+1/m^2)(m+1/m)*0
=0

m+1/m=-2 两边同乘以m m²+2m+1=0 即 (m+1)²=0 m=-1
所以带入数据
1. =1

2. =0

由m+1/m=-2知，m=-1
1.原式=2
1.原式=0