Помогите, пожалуйста

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37 просмотров

Помогите, пожалуйста


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Алгебра (19 баллов) | 37 просмотров
Дан 1 ответ
0 голосов

(1)
(x-2)*(x^2+9x)=10*(x-2)\\\\
(x-2)*(x^2+9x)-10(x-2)=0\\\\
(x-2)*(x^2+9x-10)=0\\\\
(x-2)*[x^2-x+10x-10]=0\\\\
(x-2)*[x(x-1)+10(x-1)]=0\\\\
(x-2)*[(x+10)*(x-1)]=0\\\\
(x-2)*(x+10)*(x-1)=0\\\\
x-2=0\ \ or\ \ x+10=0\ \ or\ \ x-1=0\\\\
x=2\ \ or\ \ x=-10\ \ or\ \ x=1

Ответ: 2,\ -10,\ 1
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(2)
(x+5)^2*(x-3)=(x+5)*9\\\\
(x+5)^2*(x-3)-(x+5)*9=0\\\\
(x+5)*[(x+5)*(x-3)-9]=0\\\\
(x+5)*[x^2-3x+5x-15-9]=0\\\\
(x+5)*[x^2+2x-24]=0\\\\
(x+5)*[x^2+6x-4x-24]=0\\\\
(x+5)*[x*(x+6)-4*(x+6)]=0\\\\
(x+5)*[(x+6)*(x-4)]=0\\\\
(x+5)*(x+6)*(x-4)=0\\\\
x=-5\ \ or\ \ x=-6\ \or\ \ x=4

Ответ: -5,\ -6,\ 4
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(3)
(x^2-2x+1)*(x+6)=(x-1)*8\\\\
(x-1)^2*(x+6)-8*(x-1)=0\\\\
(x-1)*[(x-1)*(x+6)-8]=0\\\\
(x-1)*[x^2+6x-x-6-8]=0\\\\
(x-1)*[x^2+5x-14]=0\\\\
(x-1)*[x^2+7x-2x-14]=0\\\\
(x-1)*[x*(x+7)-2*(x+7)]=0\\\\
(x-1)*[(x-2)*(x+7)]=0\\\\
x=1\ \ or\ \ x=2\ \or\ \ x=-7

Ответ: 1,\ 2,\ -7
------------------
(4)
x^3-x^2=7x^2-7x\\\\
x^2(x-1)=7x(x-1)\\\\
x^2*(x-1)-7x*(x-1)=0\\\\
(x^2-7x)*(x-1)=0\\\\
x*(x-7)*(x-1)=0\\\\
(x-0)*(x-7)*(x-1)=0\\\\
x=0\ \ or\ \ x=7\ \ or\ \ x=1

Ответ: 0,\ 7,\ 1

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