Question

giải phương trình :
\(3^{x+1}+2x.3^x-18x-27=0\)

Answer 1

\(3^{x+1}+2x.3^x-18x-27=0\)

\(\Leftrightarrow3^x\left(2x+3\right)-9\left(2x+3\right)=0\)

\(\Leftrightarrow\left(2x+3\right)\left(3^x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+3=0\\3^x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=2\end{matrix}\right.\)

Vậy ...............

Answer 2

3^x.3+2x.3^x-(18x+27)=0

=> 3^x(3+2x)-9.(3+2x)=0

=> (3^x-9).(3+2x)=0

=> \(\left[{}\begin{matrix}3^x-9=0\\3+2x=0\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}3^x=9=3^2\\2x=-3\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)