若x/(x^2-x-1)=1/2,则分式x^2/(x^4+x^2+1)的值为() A.1/12 B.12 C.8 D.1/8
问题描述:
若x/(x^2-x-1)=1/2,则分式x^2/(x^4+x^2+1)的值为() A.1/12 B.12 C.8 D.1/8
答
x/(x^2-x-1)=1/22x=x²-x-1x²-3x-1=0除以x得x-3-1/x=0x-1/x=3(x^4+x^2+1)÷x²=x²+1+1/x²=x²-2+1/x²+3=(x-1/x)²+3=3²+3=12∴x^2/(x^4+x^2+1)=1/12选A