Question

已知a是方程x^2-3x+1=0的根,则a^2/(a^4+1)=__________.

Answer 1

已知a是方程x^2-3x+1=0的根则：
a^2-3a+1=0；
a^4+1=a^2(a^2-3a+1)+3a^3-a^2+1
=0+3a(a^2-3a+1)+9a^2-3a-a^2+1
=0+0+7a^2+(a^2-3a+1)
=7a^2
故a^2/(a^4+1)=a^2/7a^2=7.