> 数学 >
已知x为实数,且x2+
1
x2
=3,则x3+
1
x3
的值是 ___ .
人气:335 ℃ 时间:2020-06-02 22:54:22
解答
∵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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