问题 解答题
已知|
a
|=4
|
b
|=
3
a
-
b
=6
,求
(1)(
a
-
b
)-
b

(2)求|
a
+
b
|

(提示:|
a
|2=
a
-
a
答案

(1)∵|

a
|=4,|
b
|=
3
a
b
=6

(

a
-
b
)•
b
=
a
b
-
b
b
…(1分)

=6-|

b
|2=6-3=3…(5分)

(2)∵|

a
+
b
|=
(
a
+
b
)
2
…(7分)

(

a
+
b
)2=
a
2
+2
a
b
+
b
2
=|
a
|2+2
a
b
+|
b
|2=42+2×6+(
3
)2=31…(9分)

|

a
+
b
|=
(
a
+
b
)
2
=
31
…(10分)

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