X/(X^2-3X+1)=7,求X^2/(X^4+5X^2+1)的值

题目

X/(X^2-3X+1)=7,求X^2/(X^4+5X^2+1)的值

答案

X/(X^2-3X+1)=7
(x²-3x+1)/x=1/7
即x-3+1/x=1/7
x+1/x=22/7
(x^4+5x²+1)/x²
=x²+5+1/x²
=(x+1/x)²+3
=(22/7)²+3
=631/49
∴X^2/(X^4+5X^2+1)=49/631