Question

Tìm x biết x

1) (2x - 3)'2 - (x - 1)'2 =0

2) (2x + 1)'2 - (x - 1)'2 =0

3) (3x- 5)'2 - (x + 1)'2 =0

4) (x + 2)'2 - (2x - 5)'2 =0

5) (3x - 1)'2 - (x + 5)'2 =0

6) (2x - 3)'2 - (x + 5)'2 =0

7) (3x - 4)'2 - (x + 2)'2 =0

8) (2x - 1)'2 - (3 - x)'2 =0

Answer 1

\(1)\left(2x-3\right)^2-\left(x-1\right)^2=0\\ \Leftrightarrow\left(2x-3-x+1\right)\left(2x-3+x-1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(3x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\3x=4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\\ 2)\left(2x+1\right)^2-\left(x-1\right)^2=0\\ \Leftrightarrow\left(2x+1-x+1\right)\left(2x+1+x-1\right)=0\\ \Leftrightarrow3x\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x=0\\x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\\ 3)\left(3x-5\right)^2-\left(x+1\right)^2=0\\ \Leftrightarrow\left(3x-5-x-1\right)\left(3x-5+x+1\right)=0\\ \Leftrightarrow\left(2x-6\right)\left(4x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x=6\\4x=4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\\ 4)\left(x+2\right)^2-\left(2x-5\right)^2=0\\ \Leftrightarrow\left(x+2-2x+5\right)\left(x+2+2x-5\right)=0\\ \Leftrightarrow\left(7-x\right)\left(3x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\3x=3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\x=1\end{matrix}\right.\)

Answer 2

\(5)\left(3x-1\right)^2-\left(x+5\right)^2=0\\ \Leftrightarrow\left(3x-1-x-5\right)\left(3x-1+x+5\right)=0\\ \Leftrightarrow\left(2x-6\right)\left(4x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x=6\\4x=-4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\\ 6)\left(2x-3\right)^2-\left(x+5\right)^2=0\\ \Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\\ \Leftrightarrow\left(x-8\right)\left(3x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=8\\3x=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\\ 7)\left(3x-4\right)^2-\left(x+2\right)^2=0\\ \Leftrightarrow\left(3x-4-x-2\right)\left(3x-4+x+2\right)=0\\ \Leftrightarrow\left(2x-6\right)\left(4x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x=6\\4x=2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{1}{2}\end{matrix}\right.\\ 8)\left(2x-1\right)^2-\left(3-x\right)^2=0\\ \Leftrightarrow\left(2x-1-3+x\right)\left(2x-1+3-x\right)=0\\ \Leftrightarrow\left(3x-4\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x=4\\x=-2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-2\end{matrix}\right.\)