a) \(2x^2-3x=0\)

\(\Leftrightarrow x\left(2x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x=3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\end{matrix}\right.\)

b) \(x^3-2x=0\)

\(\Leftrightarrow x\left(x^2-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{2}\end{matrix}\right.\)

c) \(x^6+1=0\)

\(\Leftrightarrow x^6=-1\)

Ta có : \(x^6\ge0\) với mọi x

Mà : -1 < 0

=> Vô nghiệm

d) \(x^3+2x=0\)

\(\Leftrightarrow x\left(x^2+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=-2\left(loại\right)\end{matrix}\right.\)

e) \(x^5+8x^2=0\)

\(\Leftrightarrow x^2\left(x^3+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x^3+8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^3=-8\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)

f) \(x^2\left(x^2-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x^2-9=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm3\end{matrix}\right.\)

g) \(\left(x+\dfrac{1}{2}\right)\left(x^2-\dfrac{4}{5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=0\\x^2-\dfrac{4}{5}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{2}\\x^2=\dfrac{4}{5}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{2}\\x=\sqrt{\dfrac{4}{5}}\end{matrix}\right.\)