Question

已知x/x^2+1=2/5求x^2/x^4+1的值，x/x^2+1=2/5(x≠0），1/x+1/x=2/5,即x+x/1=2/5,x^2/x^4+1=1/x^2+1/x^-2

=4/17,解答x/x^2-3x+1=2,求x^2/x^4+x^2+1的值

Answer 1

(1)x/x^2+1=2/5
x+1/x=5/2
x^2+1/x^2+2=25/4
x^2+1/x^2=17/4
x^2/x^4+1=4/17
(2)x/x^2-3x+1=2
x-3+1/x=1/2
x+1/x=7/2
x^2+1/x^2+2=49/4
x^2+1/x^2+1=45/4
x^2/x^4+x^2+1=4/45

追问

x^2+1/x^2+2=49/4
x^2+1/x^2+1=45/4
x^2/x^4+x^2+1=4/45
什么意思

追答

x+1/x=7/2
两侧平方得x^2+1/x^2+2=49/4
两侧减1是凑（x^4+x^2+1）/x^2=x^2+1/x^2+1
x^2/x^4+x^2+1和（x^4+x^2+1）/x^2互为倒数