Question

x3-5x=0

Answer 1

\(x^3-5x=0\\ \Leftrightarrow x\left(x^2-5\right)=0\\ \Leftrightarrow x\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)

Answer 2

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

Answer 3

\(x^3-5x=0\)

\(\Leftrightarrow x\left(x^2-5\right)=0\)

\(\Leftrightarrow x\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+\sqrt{5}=0\\x-\sqrt{5}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\sqrt{5}\\x=\sqrt{5}\end{matrix}\right.\)

Answer 4

\(\Leftrightarrow x\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)