问题 填空题
已知x为实数,且x2+
1
x2
=3,则x3+
1
x3
的值是______.
答案

∵x2+

1
x2
=(x+
1
x
)
2
-2=3,

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

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