若X+(1/X)=3,求X^2/(X^4+X^2+1)的值是：A.1/8 B.1/10 C.1/2 D.1/4方法简单易懂最好！
热心网友
X^2/(X^4+X^2+1)=1/(x^2+1+1/x^2)而x^2+1/x^2=(x+1/x)^2-2=3^2-2=7,所以X^2/(X^4+X^2+1)=1/(x^2+1+1/x^2)=1/8
热心网友
分字分母同时除以x^2得1/[x^2+1/(x^2)+1] 分母配方得1/[(x+1/x)^2-1)代入得答案为1/8
若X+(1/X)=3,求X^2/(X^4+X^2+1)的值是：A.1/8 B.1/10 C.1/2 D.1/4方法简单易懂最好！
X^2/(X^4+X^2+1)=1/(x^2+1+1/x^2)而x^2+1/x^2=(x+1/x)^2-2=3^2-2=7,所以X^2/(X^4+X^2+1)=1/(x^2+1+1/x^2)=1/8
分字分母同时除以x^2得1/[x^2+1/(x^2)+1] 分母配方得1/[(x+1/x)^2-1)代入得答案为1/8