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问题 填空题
向量
a
、
b
是单位正交基底，
c
=x
a
+y
b
，x，y∈R，（
a
+2
b
）•
c
=-4，（2
a
-
b
）•
c
=7，则x+y=______．
答案

∵

a
•
b
=0，
c
=x
a
+y
b
．

∴-4=(

a
+2
b
)•
c
=(
a
+2
b
)•(x
a
+y
b
)=x
a
2+2y
b
2+(2x+y)
a
•
b
=x+2y，

7=(2

a
-
b
)•
c
=(2
a
-
b
)•(x
a
+y
b
)=2x
a
2-y
b
2+(2y-x)
a
•
b
=2x-y．

联立

x+2y=-4
2x-y=7
，

解得

x=2
y=-3
．

∴x+y=-1．

故答案为：-1．

选择题

Mr. Smith is very happy because the cars made in his factory have never been ______.

A．popular

B．more popular

C．most popular

D．the most popular
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选择题

Don't worry if you don't understand everything, the teacher will _____ the main points at the end.[ ]

A. recover

B. review

C. require

D. remember

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