Question

Answer 1

\(10\Leftrightarrow x\left(x^2-4x+4\right)=0\Leftrightarrow x\left(x-2\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\\ 11,\Leftrightarrow\left(x-3\right)\left(5x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{2}{5}\end{matrix}\right.\\ 12,\Leftrightarrow\left(2x+3-x+1\right)\left(2x+3+x-1\right)=0\\ \Leftrightarrow\left(x+4\right)\left(3x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{2}{3}\end{matrix}\right.\\ 13,\Leftrightarrow\left(x+3\right)\left(x-3-4\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x-7\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=7\end{matrix}\right.\)

Answer 2

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

11) \(\Leftrightarrow5x\left(x-3\right)-2\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(5x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{2}{5}\end{matrix}\right.\)

12) \(\Leftrightarrow\left[{}\begin{matrix}2x+3=x-1\\2x+3=1-x\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{2}{3}\end{matrix}\right.\)

13 \(\Leftrightarrow\left(x-3\right)\left(x+3\right)-4\left(x+3\right)=0\\\Leftrightarrow\left(x+3\right)\left(x-7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-3\\x=7\end{matrix}\right.\)

Answer 3

10) \(\Rightarrow x^3-4x^2+4x=0\)

\(\Rightarrow x\left(x^2-4x+4\right)=0\Rightarrow x\left(x-2\right)^2=0\)

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

11) \(\Rightarrow\left(x-3\right)\left(5x-2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{2}{5}\end{matrix}\right.\)

12) \(\Rightarrow\left(2x+3-x+1\right)\left(2x+3+x-1\right)=0\)

\(\Rightarrow\left(x+4\right)\left(3x+2\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{2}{3}\end{matrix}\right.\)

13) \(\Rightarrow\left(x-3\right)\left(x+3\right)-4\left(x+3\right)=0\)

\(\Rightarrow\left(x+3\right)\left(x-7\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=7\end{matrix}\right.\)

Answer 4

10) \(x^3+4x=4x^2\Leftrightarrow x^3-4x^2+4x=0\Leftrightarrow x\left(x^2-4x+4\right)=0\)

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

11)\(5x\left(x-3\right)-2x+6=0\Leftrightarrow5x\left(x-3\right)-2\left(x-3\right)=0\Leftrightarrow\left(x-3\right)\left(5x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{2}{5}\end{matrix}\right.\)

12) \(\left(2x+3\right)^2=\left(x-1\right)^2\Leftrightarrow2x+3=x-1\Leftrightarrow x=-4\)

13) \(x^2-9-4\left(x+3\right)=0\Leftrightarrow\left(x-3\right)\left(x+3\right)-4\left(x+3\right)=0\Leftrightarrow\left(x+3\right)\left(x-7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=7\end{matrix}\right.\)