Question

Помогите, пожалуйста

Answer 1

(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: $1,\ 2,\ -7$
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(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: $0,\ 7,\ 1$