( 2x - 15 ) ^5 = ( 2x - 15 ) ^3
=>( 2x - 15 ) ^5 - ( 2x - 15 ) ^3 = 0
=>( 2x - 15 ) ^2 =0
=> 2x-15 = 0
=> x = \(\frac{15}{2}\) =7 \(\frac{1}{2}\)
\(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\left[\left(2x-15\right)^2-1=0\right]\)
\(\Leftrightarrow\orbr{\begin{cases}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-15=0\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x-15=0\\2x-15=1\\2x-15=-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=\frac{15}{2}\\x=8\\x=7\end{cases}}\)
P/s : ở 2 dòng cuối đổi \(\hept{\begin{cases}\\\\\end{cases}}\)thành \(\orbr{\begin{cases}\\\end{cases}}\)
=> (2x-15)^5 - (2x-15)^3 = 0
=> (2x-15)^2 . (2x-15)^3 - (2x-15)^3 = 0
=> [(2x-15)^2 - 1 ] . (2x-15)^3 = 0
=> (2x-15)^2 - 1 = 0 (cái này suy ra 2 cái)
(2x-15)^3 = 0
+Nếu (2x-15)^2 - 1 = 0
=>(2x-15)^2 = 1
=> 2x-15 = 1 (cái này suy ra 2 cái)
2x - 15 = -1
+Nếu 2x - 15 = 1
2x = 1 +15 = 16
x = 16 : 2 = 8
+Nếu 2x - 15 = -1
2x = -1 + 15 = 14
x= 14 : 2 = 7
+Nếu (2x-15)^3 = 0
2x - 15 = 0
2x = 0 + 15 = 15
x = 15 : 2 (loại)
Vậy.............
k cho t nha
