问题 填空题
已知a+
1
a
=7,a2+
1
a2
+
a
+
1
a
的值是______.
答案

∵a+

1
a
=7,

a2+

1
a2
=(a+
1
a
)2-2=49-2=47,

(

a
+
1
a
)2=a+
1
a
+2=7+2=9,

a
+
1
a
=3,
a
+
1
a
=-3(不合题意舍去),

a2+

1
a2
+
a
+
1
a
=47+3=50.

单项选择题
单项选择题