若X^2-5X-1=0,求分式X^2/(X^4+X^2+1)的值_数学解答

若X^2-5X-1=0,求分式X^2/(X^4+X^2+1)的值

人气：466 ℃　时间：2020-05-13 15:17:29

解答

X2-5x=1,
X(x-5)=1,
x-5=1/x,
x-1/x=5,
(x-1/x)2=25,
X2-2+1/x2=25,
X2+1/x2=27,
原式=1/{x2+1+(1/x2)}=1/27+1=1/28.