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问题 解答题
在△ABC中，角A，B，C的对边分别为a，b，c，已知sinAsinB+sinBsinC+cos2B=1．
（1）求证：a，b，c成等差数列；
（2）若C=
2π
3
，求
a
b
的值．
答案

（1）在△ABC中，角A，B，C的对边分别为a，b，c，

∵已知sinAsinB+sinBsinC+cos2B=1，

∴sinAsinB+sinBsinC=2 sin2B．

再由正弦定理可得 ab+bc=2b2，即 a+c=2b，故a，b，c成等差数列．

（2）若C=

2π
3
，由（1）可得c=2b-a，由余弦定理可得 （2b-a）2=a2+b2-2ab•cosC=a2+b2+ab．

化简可得 5ab=3b2，∴

a
b
=
3
5
．

完形填空

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 小题4: way is to look for good points in other people. You will find most people pleasant to go with and it will surely make you happy. Third, you can’t expect to be too perfect,   小题5: don’t be too unhappy when you make a mistake. Everything will be OK 小题6: you try to make things right. Finally, it’s important to remember that while you are no worse 小题7: others, chances you have may not be much better.   小题8: this case, the surest way to be happy is to hold optimistic attitude.
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单项选择题

严格控制钢材及焊接材料的（），能防止热裂纹的产生。

A.硫、磷含量

B.链含量

C.氮、氢含量

D.镇、络含量
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