Question

若x/x^2-3x+1=2,求分式x^2/x^4+x^2+1的值

Answer 1

x/x^2-3x+1=2

则(x^2-3x+1)/x=1/2

所以x-3+1/x=1/2

所以x+1/x=7/2

两边平方,得x²+1/x²+2=49/4

所以x²+1/x²=41/4

分式x^2/x^4+x^2+1=1/(x²+1+1/x²)=1/(41/4+1)=4/45