Question

计算较麻烦、若x=4-根号7/3,求x^2/x^4+x^2+1的值

Answer 1

x=(4-√7)/3

1/x=3/(4-√7)=(4+√7)/3

x+1/x=8/3

取原式的倒数

（x^4+x^2+1）/x^2

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

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

=(8/3)^2 -1

=55/9

所以原式=9/55