[tex]A=1/2*| \left|\begin{array}{ccc}2^{n}&3^{n}&1\\2^{n+1}&3^{n+1}&1\\2^{n+2}&3^{n+2}&1\end{array}\right||=1/2*| \left|\begin{array}{ccc}2^{n}&3^{n}&1\\2^{n}*2&3^{n}*3&1\\2^{n}*4&3^{n}*9&1\end{array}\right||=[/tex]
[tex]1/2*|2^{n}*3^{n}* \left|\begin{array}{ccc}1&1&1\\2&3&1\\4&9&1\end{array}\right|| =1/2*|6^{n}*(3+18+4-12-9-2)|= [/tex]
[tex]=1/2*|6^{n}*2|[/tex]
Dar aria este 216, deci avem:
[tex]1/2*|6^{n}*2|=216 =\ \textgreater \ |6^n*2|=432
[/tex]
Caz 1:
[tex]6^{n}*2=432 =\ \textgreater \ 6^n=216 =\ \textgreater \ n=3[/tex]
Caz 2:
[tex]6^{n}*2=-432 =\ \textgreater \ 6^n=-216[/tex]
Ecuatia nu are solutii, deoarece un numar pozitiv ridicat la orice putere nu are ca rezultat un numar negativ.
n=3
