题目内容

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
(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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