a, \(\left(3n+2\right)^4=\left(3n+2\right)^6\)
\(\Rightarrow\left(3n+2\right)^6-\left(3n+2\right)^4=0\)
\(\Rightarrow\left(3n+2\right)^4\left[\left(3n+2\right)^2-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(3n+2\right)^4=0\\\left(3n+2\right)^2-1=0\end{matrix}\right.\)
+) \(\left(3n+2\right)^4=0\Rightarrow n=\dfrac{-2}{3}\)
+) \(\left(3n+2\right)^2-1=0\Rightarrow\left[{}\begin{matrix}3n+2=1\\3n+2=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}n=\dfrac{-1}{3}\\n=-1\end{matrix}\right.\)
Vậy...
b, \(6^n+6^{n+1}=252\)
\(\Rightarrow6^n+6^n.6=252\)
\(\Rightarrow6^n.7=252\)
\(\Rightarrow6^n=36\Rightarrow n=2\)
Vậy n = 2
c, \(5^{n-2}+3.5^{n-2}=500\)
\(\Rightarrow5^{n-2}.4=500\)
\(\Rightarrow5^{n-2}=125\)
\(\Rightarrow n-2=3\)
\(\Rightarrow n=5\)
Vậy n = 5
