Question

已知实数a,满足a的平方减a减1为0求a的八次方加7a的-4次方

Answer 1

a^2-a-1=0 a^2=a+1 a^4=(a+1)^2=a^2+2a+1=3a+2

a^8-7a^4=a^4(a^4-7)=(3a+2)(3a-5)=9a^2-9a-10=9(a^2-a-1)-1=-1