已知实数x满足x2+1x2+x+1x=0，那么x+1x的值是（）A.1或-2B.-1或2C.1D.-2

Question

已知实数x满足x²+(1)/(x2)+x+(1)/(x)=0，那么x+(1)/(x)的值是（　　）
A. 1或-2
B. -1或2
C. 1
D. -2

Answer 1

∵x²+(1)/(x2)+x+(1)/(x)=0
∴(x+(1)/(x))2−2+x+(1)/(x)＝0
∴[（x+(1)/(x)）+2][（x+(1)/(x)）-1]=0
∴x+(1)/(x)=1或-2．
∵x+(1)/(x)=1无解，
∴x+(1)/(x)=-2．
故选D．