早教吧 育儿知识 作业答案 考试题库 百科 知识分享

已知x+1x=3,求x4+1x4,x6+1x6.

题目详情
已知x+
1
x
=3,求x4+
1
x4
x6+
1
x6
▼优质解答
答案和解析
∵x2+
1
x2
=(x+
1
x
2-2=9-2=7,
∴x4+
1
x4
=(x2+
1
x2
2-2=49-2=47;
∴(x2+
1
x2
)(x4+
1
x4
)=x6+x2+
1
x2
+
1
x6

∴x6+
1
x6
=7×47-7=322.