Question

若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值

Answer 1

x/(x²-3x+1)=2

得 1/(x-3+1/x)=2

x-3+1/x=1/2

x+1/x=7/2

x²/x^4+x²+1=1/(x²+1+1/x²)

=1/[(x+1/x)²-1]

=1/(49/4-1)

=4/45