已知x为实数,且x2+1x2=3,则x3+1x3的值是______.-数学

题目简介

已知x为实数,且x2+1x2=3,则x3+1x3的值是______.-数学

题目详情

已知x为实数,且x2+
1
x2
=3,则x3+
1
x3
的值是______.
题型:填空题难度:中档来源:不详

答案

∵x2+class="stub"1
x2
=(x+class="stub"1
x
)
2
-2=3,
class="stub"1
x
+x=±
5

又∵x3+class="stub"1
x3
=(x+class="stub"1
x
)(x2-1+class="stub"1
x2
)=±
5
×2
=±2
5

故答案为:±2
5

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