Question

已知x²-3x+1=0,求分式x²/x⁴+x²+1的值

Answer 1

x⁴+x²+1/x²=x²+1+1/x² (1)

x²-3x+1=0,可知X不等于0

则除以X 即 x²-3x+1/X=X-3-1/X=0

X-1/X=3

x²-2+1/x²=9

x²+1/x²=7(2

(2)代入(1)中可得 x⁴+x²+1/x²=8

由倒数的概念可知：原式=1/8