已知x为实数，且x2+1x2=3，则x3+1x3的值是．

Question

已知x为实数，且x²+(1)/(x2)=3，则x³+(1)/(x3)的值是 ___ ．

Answer 1

∵x²+(1)/(x2)=(x+(1)/(x))2-2=3，
故(1)/(x)+x=±√(5)，
又∵x³+(1)/(x3)=（x+(1)/(x)）（x²-1+(1)/(x2)）=±√(5)×2
=±2√(5)．
故答案为：±2√(5)．