a ) \(x^3+3x^2+3x+2=0\)
\(\Leftrightarrow x^3+3x^2+3x+1+1=0\)
\(\Leftrightarrow\left(x+1\right)^3+1=0\)
\(\Leftrightarrow\left(x+1\right)^3=-1\)
\(\Leftrightarrow x+1=-1\)
\(\Leftrightarrow x=-2\)
Vậy \(x=-2\)
b ) \(x^4-2x^3+2x-1=0\)
\(\Leftrightarrow x^4-1-2x\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^2+1-2x\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)^3\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
a, \(x^3+3x^2+3x+2=0\)
\(\Leftrightarrow\left(x^3+2x^2\right)+\left(x^2+2x\right)+\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2+x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x^2+x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=0\end{matrix}\right.\)
b, \(x^4-2x^3+2x-1=0\)
\(\Leftrightarrow\left(x^4-x^3\right)-\left(x^3-x^2\right)-\left(x^2-x\right)+\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[\left(x^3-x^2\right)\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)^3=0\)
\(\Leftrightarrow x=1\)
a ) x^3+3x^2+3x+2=0x3+3x2+3x+2=0
\Leftrightarrow x^3+3x^2+3x+1+1=0⇔x3+3x2+3x+1+1=0
\Leftrightarrow\left(x+1\right)^3+1=0⇔(x+1)3+1=0
\Leftrightarrow\left(x+1\right)^3=-1⇔(x+1)3=−1
\Leftrightarrow x+1=-1⇔x+1=−1
\Leftrightarrow x=-2⇔x=−2
Vậy x=-2x=−2
b ) x^4-2x^3+2x-1=0x4−2x3+2x−1=0
\Leftrightarrow x^4-1-2x\left(x^2-1\right)=0⇔x4−1−2x(x2−1)=0
\Leftrightarrow\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)=0⇔(x2−1)(x2+1)−2x(x2−1)=0
\Leftrightarrow\left(x^2-1\right)\left(x^2+1-2x\right)=0⇔(x2−1)(x2+1−2x)=0
\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-1\right)^2=0⇔(x−1)(x+1)(x−1)2=0
\Leftrightarrow\left(x-1\right)^3\left(x+1\right)=0⇔(x−1)3(x+1)=0
\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x=-1\end{matrix}\right.⇔[(x−1)3=0x+1=0⇔[x−1=0x=−1
\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.⇔[x=1x=−1
Vậy \left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.[x=1x=−1
a ) x^3+3x^2+3x+2=0x3+3x2+3x+2=0
\Leftrightarrow x^3+3x^2+3x+1+1=0⇔x3+3x2+3x+1+1=0
\Leftrightarrow\left(x+1\right)^3+1=0⇔(x+1)3+1=0
\Leftrightarrow\left(x+1\right)^3=-1⇔(x+1)3=−1
\Leftrightarrow x+1=-1⇔x+1=−1
\Leftrightarrow x=-2⇔x=−2
Vậy x=-2x=−2
b ) x^4-2x^3+2x-1=0x4−2x3+2x−1=0
\Leftrightarrow x^4-1-2x\left(x^2-1\right)=0⇔x4−1−2x(x2−1)=0
\Leftrightarrow\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)=0⇔(x2−1)(x2+1)−2x(x2−1)=0
\Leftrightarrow\left(x^2-1\right)\left(x^2+1-2x\right)=0⇔(x2−1)(x2+1−2x)=0
\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-1\right)^2=0⇔(x−1)(x+1)(x−1)2=0
\Leftrightarrow\left(x-1\right)^3\left(x+1\right)=0⇔(x−1)3(x+1)=0
\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x=-1\end{matrix}\right.⇔[(x−1)3=0x+1=0⇔[x−1=0x=−1
\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.⇔[x=1x=−1
Vậy \left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.[x=1x=−1
a ) x3+3x2+3x+2=0x3+3x2+3x+2=0
⇔x3+3x2+3x+1+1=0⇔x3+3x2+3x+1+1=0
⇔(x+1)3+1=0⇔(x+1)3+1=0
⇔(x+1)3=−1⇔(x+1)3=−1
⇔x+1=−1⇔x+1=−1
⇔x=−2⇔x=−2
Vậy x=−2x=−2
b ) x4−2x3+2x−1=0x4−2x3+2x−1=0
⇔x4−1−2x(x2−1)=0⇔x4−1−2x(x2−1)=0
⇔(x2−1)(x2+1)−2x(x2−1)=0⇔(x2−1)(x2+1)−2x(x2−1)=0
⇔(x2−1)(x2+1−2x)=0⇔(x2−1)(x2+1−2x)=0
⇔(x−1)(x+1)(x−1)2=0⇔(x−1)(x+1)(x−1)2=0
⇔(x−1)3(x+1)=0⇔(x−1)3(x+1)=0
⇔[(x−1)3=0x+1=0⇔[x−1=0x=−1⇔[(x−1)3=0x+1=0⇔[x−1=0x=−1
⇔[x=1x=−1⇔[x=1x=−1
Vậy [x=1x=−1