18．若实数m满足m²－ √10 × m + 1 = 0,则 m的四次方+ m的负四次方 =

题目

18．若实数m满足m²－ √10 × m + 1 = 0,则 m的四次方+ m的负四次方 =
RT,

答案

m²-√10m+1=0
两边除以m得m+1/m=√10
m^4+1/m^4
=(m²+1/m²)²-2
=[(m+1/m)²-2]²-2
=[(√10)²-2]²-2=62