已知xx2+x+1＝a（a≠0且a≠12），试求分式x2x4+x2+1的值．

Question

已知(x)/(x2+x+1)＝a（a≠0且a≠(1)/(2)），试求分式(x2)/(x4+x2+1)的值．

Answer 1

∵(x)/(x2+x+1)=(1)/(x+(1)/(x)+1)=a，
∴x+(1)/(x)=(1)/(a)-1，
则原式=(1)/(x2+(1)/(x2)+1)=(1)/((x+(1)/(x))2−1)=(1)/(((1)/(a)−1)2−1)=(1)/((1)/(a2)−(2)/(a))=(a2)/(1−2a)．