Ecuatie in x si y cu puteri

catalina17 Mar Oct 02, 2012 12:28 am

Sa se rezolve in N ecuatia 3^x + 3^y = 90

Va rog explicati-mi cum se fac aceste exercitii!

Multumesc!

**Admin** Joi Oct 04, 2012 9:24 pm

$\begin{array}{l} {3^x} + {3^y} = 90\left| { \div {3^2}} \right. \Rightarrow {3^{x - 2}} + {3^{y - 2}} = 10\mathop \Rightarrow \limits^{x,y \in {\rm{N}}} \,\left\{ \begin{array}{l} {3^{x - 2}} = 9\\ {3^{y - 2}} = 1 \end{array} \right. \vee \left\{ \begin{array}{l} {3^{x - 2}} = 1\\ {3^{y - 2}} = 9 \end{array} \right. \Rightarrow \\ \left( {x,y} \right) \in \left\{ {\left( {4,2} \right),\left( {2,4} \right)} \right\} \end{array}$
Semnul ${\color{Red} \mathbf\vee}$ inseamna sau.

Ecuatie in x si y cu puteri

Ecuatie in x si y cu puteri

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