Question

已知实数x满足x方＋x方分之1减3x减x分之3减8等于0,求x加x分之1的值

Answer 1

设x+1/x=t,平方得:x^2+1/x^2+2=t^2

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

原方程变为:

(t^2-2)-3t-8=0

t^2-3t-10=0

(t-5)(t+2)=0

t=5或t=-2.

即x+1/x=5或-2