1: \(\dfrac{x}{2}+\dfrac{x^2}{8}=0\)
=>\(\dfrac{x^2}{8}+\dfrac{4x}{8}=0\)
=>\(x^2+4x=0\)
=>x(x+4)=0
=>\(\left[{}\begin{matrix}x=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-4\end{matrix}\right.\)
2:
\(8x^3-72x=0\)
=>\(8x\left(x^2-9\right)=0\)
=>\(x\left(x^2-9\right)=0\)
=>x(x-3)(x+3)=0
=>\(\left[{}\begin{matrix}x=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)
3: \(2-x=2\left(x-2\right)^3\)
=>\(2\left(x-2\right)^3+\left(x-2\right)=0\)
=>\(\left(x-2\right)\left[2\left(x-2\right)^2+1\right]=0\)
mà \(2\left(x-2\right)^2+1>=1>0\forall x\)
nên x-2=0
=>x=2
4: \(x^8+36x^4=0\)
=>\(x^4\left(x^4+36\right)=0\)
mà \(x^4+36>=36>0\forall x\)
nên \(x^4=0\)
=>x=0
