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請教一題向量

ra+sb+c2=r2a2+s2b2+c2+2rsab+2rac+2sbc

=3r2+5s2+33+2rs+2r18s

=3r2+2(s+1)r+5s218s+33

=3(r+3s+1)2+5s218s+333s2+2s+1

=3(r+3s+1)2+314(s24s+7)

=3(r+3s+1)2+314(s2)2+1414

且當 ``= 成立時, r+3s+1=s2=0

亦即,當 s=2r=1 時,ra+sb+c 有最小值 14 

多喝水。

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