1, \(\left(x-1\right)^2=4\)
\(\Leftrightarrow\left(x-1\right)^2-4=0\)
\(\Leftrightarrow\left(x-1\right)^2-2^2=0\)
\(\Leftrightarrow\left(x-1-2\right)\left(x-1+2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
\(\Rightarrow S=\left\{3;-1\right\}\)
2, \(\left(x-1\right)^2=9\left(x+1\right)^2\)
\(\Leftrightarrow\left(x-1\right)^2-9\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)^2-\left[3\left(x+1\right)\right]^2=0\)
\(\Leftrightarrow\left[x-1-3\left(x+1\right)\right]\left[x-1+3\left(x+1\right)\right]=0\)
\(\Leftrightarrow\left(x-1-3x-3\right)\left(x-1+3x+3\right)=0\)
\(\Leftrightarrow\left(-2x-4\right)\left(4x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x-4=0\\4x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-2x=4\\4x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{-1}{2}\end{matrix}\right.\)
\(\Rightarrow S=\left\{-2;\dfrac{-1}{2}\right\}\)
3, \(x\left(x-1\right)=-x\left(x+3\right)\)
\(\Leftrightarrow x^2-x=-x^2-3x\)
\(\Leftrightarrow x^2-x+x^2+3x=0\)
\(\Leftrightarrow2x^2+2x=0\)
\(\Leftrightarrow2x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
\(\Rightarrow S=\left\{0;-1\right\}\)
4, \(\left(2x-1\right)^2=9\)
\(\Leftrightarrow\left(2x-1\right)^2-9=0\)
\(\Leftrightarrow\left(2x-1\right)^2-3^2=0\)
\(\Leftrightarrow\left(2x-1-3\right)\left(2x-1+3\right)=0\)
\(\Leftrightarrow\left(2x-4\right)\left(2x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-4=0\\2x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=-2\end{matrix}\right.\Leftrightarrow}\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
Xin lỗi nhiều nha.
Máy tính mik bị sao í
