问题 解答题
已知x+
1
x
=4,不求x的值,求下列各式的值:
(1)x2+
1
x2

(2)(x-
1
x
2
答案

(1)x2+

1
x2
=x2+2x•
1
x
+
1
x2
-2x•
1
x

=(x+

1
x
2-2

=42-2

=14;

(2)(x-

1
x
2

=x2-2x•

1
x
+
1
x2

=x2+2x•

1
x
+
1
x2
-4x•
1
x

=(x+

1
x
2-4

=16-4

=12.

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