(2x+y)a -3yb=4xa +( x-4y +1)b ;
(2x+y -4x)a =(3y +x-4y +1)b ;
(y -2x)a =(x-y +1)b ;
Т.к. a и b не коллинеарны, то:
{ y -2x = 0 ; x-y +1 =0 ⇔{ y=2x ; x -2x+1 =0. {y =2*1; x =1.
ответ : x =1 , y=2 .
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Дано: BM/MC =2:1 ; M∈BC ; AO =OM , O∈AM.
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Доказать: BO =(1/2)*BA +(1/3)*BC .
BO =BA+AO =BA+AM/2 ;
AM = AB+BM =AB +(2/3)BC ⇒ AM/2 =(1/2)*AB +(1/3)*BC.
BO =BA+AM/2 =BA+(1/2)*AB +(1/3)*BC =BA - (1/2)*BA +(1/3)*BC =
(1/2)*BA +(1/3)*BC .
BO = (1/2)*BA +(1/3)*BC .