Question

若x分之一+x=3,求（x的4次方+x的二次方+x分之1的2次方）分之一.急求

Answer 1

1/x + x = 3

x^2-3x+1=0

x=(3±根号5)/2

x^2=3x-1=3±根号5

x^4=14±2根号5

1/x + x = 3

(1/x + x)^2 = 3^2

1/x^2 + 2 + x^2 = 9

1/x^2 + x^2 = 7

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

= 1 / { x^4 +（x^2 + 1/x^2 }

= 1 / { x^4 +（x^2 + 1/x^2 }

= 1 / { 14±2根号5 +7 }

= 1/ (21±2根号5)

= (21±2根号5) / {21^2-(2根号5)^2}

= (21±2根号5) / 411