Question

x分之1+x=3,则x的四次方+x的平方+1分之x的平方

Answer 1

x^2/(x^4+x^2+1) 取倒数

(x^4+x^2+1)/x^2

=x^2+1+1/x^2

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

=(x+1/x)^2-1

=3^2-1

=8 (取倒数)

所以x^2/(x^4+x^2+1)=1/8