若x/(x^2-x+1)=4,求分式x^2/(x^4+x^2+1)的值
问题描述:
若x/(x^2-x+1)=4,求分式x^2/(x^4+x^2+1)的值
答
∵x/(x^2-x+1)=4∴﹙x²-x+1﹚/x=1/4x+1/x=5/4x²+2+1/x²=25/16x²+1/x²=﹣7/16∵﹙ x^4+x²+1﹚/x²=x²+1/x²+1=﹣7/16+1=9/16∴ x²/﹙x^4+x²...