Sửa đề: \(a.2x^3+2x+x^2+1=0\)
\(\Leftrightarrow\left(2x^3+2x\right)+\left(x^2+1\right)=0\)
\(\Leftrightarrow2x\left(x^2+1\right)+\left(x^2+1\right)=0\)
\(\Leftrightarrow\left(x^2+1\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+1=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2=-1\left(vl\right)\\x=-\dfrac{1}{2}\left(tm\right)\end{matrix}\right.\)
Vậy, \(x=\dfrac{-1}{2}\)
\(b.x^7+x^3+2x^5+2x=0\)
\(\Leftrightarrow\left(x^7+x^3\right)+\left(2x^5+2x\right)=0\)
\(\Leftrightarrow x^3\left(x^4+1\right)+2x\left(x^4+1\right)=0\)
\(\Leftrightarrow\left(x^4+1\right)\left(x^3+2x\right)=0\)
\(\Leftrightarrow x\left(x^4+1\right)\left(x^2+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^4+1=0\\x^2+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x^4=-1\left(vl\right)\\x^2=-2\left(vl\right)\end{matrix}\right.\)
Vậy, \(x=0\)
a ) Sai đề : \(2x^3+2x+x^2+1=0\)
\(\Leftrightarrow2x\left(x^2+1\right)+x^2+1=0\)
\(\Leftrightarrow\left(2x+1\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=0\\x^2+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-1\\x^2=-1\left(VL\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-\dfrac{1}{2}\)
Vậy \(x=-\dfrac{1}{2}\)
b ) \(x^7+x^3+2x^5+2x=0\)
\(\Leftrightarrow x^3\left(x^4+1\right)+2x\left(x^4+1\right)=0\)
\(\Leftrightarrow\left(x^3+2x\right)\left(x^4+1\right)=0\)
\(\Leftrightarrow x\left(x^2+2\right)\left(x^4+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+2=0\\x^4+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=-2\left(VL\right)\\x^4=-1\left(VL\right)\end{matrix}\right.\)
Vậy \(x=0\)