Để \(3;x-2;27\) là một cấp số nhân thì:
\(\left(x-2\right)^2=3\cdot27\)
\(\Leftrightarrow\left(x-2\right)^2=81\)
\(\Leftrightarrow\left(x-2\right)^2=9^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=9\\x-2=-9\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-7\end{matrix}\right.\)
Vậy: \(3;x-2;27\) là cấp số nhân khi \(\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-7\end{matrix}\right.\)
\(3.n^2=27\\ \Leftrightarrow n^2=\dfrac{27}{3}=9=3^2=\left(-3\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}n=3\\n=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-2=3.3\\x-2=3.\left(-3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-2=9\\x-2=-9\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=11\\x=-7\end{matrix}\right.\)
