b: \(\left(x^2+1\right)\left(x-2\right)+2x=4\)
=>\(\left(x^2+1\right)\left(x-2\right)+2x-4=0\)
=>\(\left(x^2+1\right)\left(x-2\right)+2\left(x-2\right)=0\)
=>\(\left(x-2\right)\left(x^2+1+2\right)=0\)
=>\(\left(x-2\right)\left(x^2+3\right)=0\)
mà \(x^2+3>=3>0\forall x\)
nên x-2=0
=>x=2
d: \(\left(x+1\right)^2=x+1\)
=>\(\left(x+1\right)^2-\left(x+1\right)=0\)
=>\(\left(x+1\right)\left(x+1-1\right)=0\)
=>\(x\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
c: \(8x\left(x-2017\right)-2x+4034=0\)
=>\(8x\left(x-2017\right)-2\left(x-2017\right)=0\)
=>\(\left(x-2017\right)\left(8x-2\right)=0\)
=>\(\left[{}\begin{matrix}x-2017=0\\8x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\)
e: \(x^4+5x^3-8x-40=0\)
=>\(\left(x^4+5x^3\right)-\left(8x+40\right)=0\)
=>\(x^3\left(x+5\right)-8\left(x+5\right)=0\)
=>\(\left(x+5\right)\left(x^3-8\right)=0\)
=>\(\left[{}\begin{matrix}x+5=0\\x^3-8=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x+5=0\\x^3=8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
