一道数学题,对我来说挺难已知X/(X^2+X+1)=a求X^2/(X^4+X^2+1)的值

芦婷婷回答：

　　X/(X^2+X+1)=a(X^2+X+1)/X=1/aX+1+1/X=1/aX+1/X=1/a-1(X+1/X)^2=(1/a-1)^2X^2+2+1/X^2=(1/a-1)^2X^2+1+1/X^2=(1/a-1)^2-1(X^4+X^2+1)/X^2=X^2+1+1=(1/a-1)^2-1=1/a^2-2/aX^2/(X^4+X^2+1)=1/(1/a^2-2/a)=a^2/(1-2a)