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\(x^3+x^2+x+1\)
\(=\left(x^3+x^2\right)+\left(x+1\right)\)
\(=x^2\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+1\right)\)
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x=9 ⇒ 10= x+1 thay vào C ta đc
C = x14- (x+1).x13 +........ - (x+1).x +x+1
⇒C = x14-x14-x13+........ -x2 -x +x+1
⇒C =1
mk làm tóm tắt ít số hơn nếu bạn muốn dễ hiểu thì thay nhiều cái vào
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Có x= 9 nên 10x^13=(9+1)x^13=(x+1)x^13=x^14+x^13
Tương tự thay vào C=x^14 - x^14 + x^13 - ....-x^2 - x +10=-x + 10=1
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Nếu \(x=9\Rightarrow10=x+1\)
Thay \(10=x+1\) vào A , ta được :
\(A=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+...+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)
\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+...+x^3+x^2-x^2-x+x+1\)
\(=1\)
Vậy \(A=1\) tại \(x=9\)
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\(x^{14}-10x^{13}+10x^{12}-10x^{11}+...+10x^2-10x+10\)
\(=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+..+\left(x+1\right)x^2-\left(x+1\right)x+x+1\)
\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+...+x^3+x^2-x^2-x+x+1\)
\(=1\)
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Ta có: x=9 ⇒10=x+1
Thay 10=x+1 vào A ta được:
A= x14-(x+1)x13 + (x+1)x12 - (x+1)x11+......-(x-1)x + (x+1)
A=x14 - x14 - x13 + x13 + x12 - x12 - x11 +.......- x2 - x + x+1
A=(x14 - x14) -( x13 - x13 )+ (x12 - x12 ) - (x11 - x11 )......- (x - x)+1
A= 1
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\(x^{14}-10x^{13}+10x^{12}-10x^{11}+...-10x+10=x^{14}-9x^{13}-x^{13}+9x^{12}+x^{12}-...-9x-x+9+1\)
\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-...-x^2-x+x+1=1\)
\(x^3-10x-12=\left(x^3-2x^2-6x\right)+\left(2x^2-4x-12\right)\)
\(=x\left(x^2-2x-6\right)+2\left(x^2-2x-6\right)=\left(x+2\right)\left(x^2-2x-6\right)\)