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a*(a+2b)=(cosa,sina)*(cosa+2cosb,sina+2sinb)
=cosacosa+2cosacosb+sinasina+2sinasinb
=1+2cos(a-b) cos(a-b)属于[-1,1]
a*(a+2b)属于[-1,3]
(a+2b)=(cosa+2cosb,sina+2sinb)
|a+2b|*|a+2b|
=cosacosa+4cosacosb+4cosbcosb+sinasina+4sinasinb+4sinbsinb
=5+4cos(a-b) a-b=pi/3 cos(a-b)=1/2
就有 |a+2b| = 根下7
1年前
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