x2-3x+1分之x=4分之1 求x4-2x2+1分之x2的值

题目

x2-3x+1分之x=4分之1 求x4-2x2+1分之x2的值

答案

x/(x^2-3x+1)=1/4
1/(x-3+1/x)=1/4
4=x+1/x-3
x+1/x=7
(x+1/x)^2=49
x^2+1/x^2+2=49
x^2+1/x^2=47
x^2/(x^4-2x^2+1)
=1/(x^2-2+1/x^2)
=1/(47-2)
=1/45