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b)\(\left|21x-5\right|=\left|3x-7\right|\)
\(\Leftrightarrow\begin{cases}21x-5=3x-7\\21x-5=7-3x\end{cases}\)
\(\Leftrightarrow\begin{cases}9x=-1\\24x=12\end{cases}\)
\(\Leftrightarrow\begin{cases}x=-\frac{1}{9}\\x=\frac{1}{2}\end{cases}\)
a)\(\left|2x-7\right|=3\)
\(\Rightarrow2x-7=\pm3\)
Nếu \(2x-7=3\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=5\)
Nếu \(2x-7=-3\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
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(3x - 7)2015 = (3x - 7)2017
(3x - 7)2017 - (3x - 7)2015 = 0
(3x - 7)2017[(3x - 7)2 - 1] = 0
=> (3x - 7)2017 = 0 hoặc (3x - 7)2 = 1
=> 3x - 7 = 0 hoặc 3x - 7 = ± 1
=> x = 7/3 hoặc x = { 8/3 ; 2 }
Vậy x = { 2; 7/3; 8/3 }
\(y\left(y^2-1\right)=0\Leftrightarrow\orbr{\begin{cases}y=0\\y^2-1=0\end{cases}}\)
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\(\frac{2x-3}{\left(7-6x\right)^2}+\frac{x-2}{\left(7-6x\right)^2}=\frac{6x-3}{\left(3x-5\right)^2}-\frac{12x-10}{\left(3x-5\right)^2}\)
\(\Leftrightarrow\frac{2x-3+x-2}{\left(7-6x\right)^2}=\frac{6x-3-12x+10}{\left(3x-5\right)^2}\)
\(\Leftrightarrow\frac{3x-5}{\left(7-6x\right)^2}=\frac{7-6x}{\left(3x-5\right)^2}\)
\(\Leftrightarrow\left(7-6x\right)^3=\left(3x-5\right)^3\)
\(\Leftrightarrow7-6x=3x-5\)
\(\Leftrightarrow7+5=3x+6x\)
\(\Leftrightarrow12=9x\)
\(\Leftrightarrow x=\frac{4}{3}\)
Vậy \(x=\frac{4}{3}\)
Ta có: \(\left(3x-7\right)^{2005}=\left(3x-7\right)^{2003}\)
\(\Leftrightarrow\left(3x-7\right)^{2005}-\left(3x-7\right)^{2003}=0\)
\(\Leftrightarrow\left(3x-7\right)^{2003}\left[\left(3x-7\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(3x-7\right)^{2003}=0\\\left(3x-7\right)^2-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x\in\left\{\frac{8}{3};2\right\}\end{cases}}\)
Vậy \(x\in\left\{\frac{7}{3};\frac{8}{3};2\right\}\)
\(\left(3x-7\right)^{2005}=\left(3x-7\right)^{2003}\)
\(\Rightarrow\left(3x-7\right)^{2005}-\left(3x-7\right)^{2003}=0\)
\(\Leftrightarrow\left(3x-7\right)^{2003}[\left(3x-7\right)^2-1]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(3x-7\right)^{2003}=0\\\left(3x-7\right)^2-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}3x-7=0\\3x-7=1\end{cases}}\)hoặc \(3x-7=-1\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x=\frac{8}{3}\end{cases}}\)hoặc \(x=2\)
Vậy ...............................