Question

Tính nghiệm của đa thức Q(x)= (x-2)²⁰¹¹ - (x-2)

Answer 1

\(\left(x-2\right)^{2011}-\left(x-2\right)=0\Leftrightarrow\left(x-2\right)\left[\left(x-2\right)^{2010}-1\right]=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^{2010}-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x-2\right)^{2010}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right..Vậy:x\in\left\{1;2;3\right\}\)

Answer 2

Q(x)=(x-2)2011-(x-2) =(x-2)(x2010 -1) =(x-2)(x2010 -x1005 +x1005 -1) =(x-2)(x1005 +1)(x1005-1) =0 x-2=0,x1005+1=0,x1005-1=0 x=2,x=1,x=-1 là các nghiệm

Answer 3

Q(x)=(x-2)²⁰¹¹-(x-2) =(x-2)(x²⁰¹⁰ -1) =(x-2)(x²⁰¹⁰ -x¹⁰⁰⁵ +x¹⁰⁰⁵ -1) =(x-2)(x¹⁰⁰⁵ +1)(x¹⁰⁰⁵-1) =0 x-2=0,x¹⁰⁰⁵+1=0,x¹⁰⁰⁵-1=0 x=2,x=1,x=-1 là các nghiệm

Answer 4

(x−2)2011−(x−2)=0⇔(x−2)[(x−2)2010−1]=0⇔[x−2=0(x−2)2010−1=0⇔[x=2(x−2)2010=1⇔⎡⎢⎣x=2x−2=1x−2=−1⇔⎡⎢⎣x=2x=3x=1.V