\(\left(2x-5\right)^5=\left(2x-5\right)^3\)
\(\left(2x-5\right)^5-\left(2x-5\right)^3=0\)
\(\left(2x-5\right)^3\left[\left(2x-5\right)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(2x-5\right)^3=0\\\left(2x-5\right)^2-1=0\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}2x-5=0\\\left(2x-5\right)^2=1=\left(\pm1\right)^2\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}2x=5\\2x-5=-1\text{ hoặc }2x-5=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{2}\\2x=4\text{ hoặc }2x=6\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=2\text{ hoặc }x=3\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{\frac{5}{2}\text{ ; }2\text{ ; }3\right\}\)
\(\left(2x-5\right)^5=\left(2x-5\right)^3\)
=>\(\left(2x-5\right)^5-\left(2x-5\right)^3=0\)
=>\(\left(2x-5\right)^3.\left\{\left(2x-5\right)^2-1\right\}=0\)
=>\(\orbr{\begin{cases}\left(2x-5\right)^3=0\\\left(2x-5\right)^2-1=0\end{cases}}\)
=>\(\orbr{\begin{cases}2x-5=0\\\left(2x-5\right)^2=1\end{cases}}\)
=>\(x=\left\{\frac{5}{2};3;2\right\}\)\(\orbr{\begin{cases}x=\frac{5}{2}\\\orbr{\begin{cases}2x-5=1\\2x-5=-1\end{cases}}\end{cases}}\)
(2x-5)5= (2x-5)3
(2x-5)5-(2x-5)3= 0
(2x-5)3.(2x-5)2-(2x-5)3.1= 0
(2x-5)3.[(2x-5)2-1]= 0
= > (2x-5)3 = 0 hoặc (2x-5)2-1= 0
+)(2x-5)3 = 0
= >2x-5= 0
2x= 0+5
2x= 5
= > x= \(\frac{2}{5}\)
+)(2x-5)2-1= 0
(2x-5)2= 1
(2x-5)2 = 12= (-1)2
= >2x-5 = 1 hoặc2x-5 = -1
+)2x-5 = 1
2x = 1+5
2x = 6
x= 6:2
x= 3
+)2x-5 = -1
2x = -1+5
2x = 4
x= 4:2
x= 2
Vậy x\(\in\){ \(\frac{2}{5}\);3;2}
