Question

已知X=(4-根号7)/3,那么求x2/(x4+x2+1) 的值

Answer 1

x=（4-√7）/3

x²=(16+7-8√7)/9=(32-8√7)/9-9/9

所以

x²=(8/3)x-1

即x²+1=(8/3)x

所以 x+1/x=8/3

(x+1/x)²=64/9

x²+1/x²+2=64/9

所以

x2/(x4+x2+1)

=1/(x²+1+1/x²)

=1/(64/9-1)

=1/(55/9)

=9/55