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Media geometrica a numerelor 3 la puterea x si 9 la puterea y este 9 . Aflati cele doua numere x si y, daca se stie ca x=y+1. VA rog ajutati-ma.

Răspuns :

[tex]3^{x}[/tex] si [tex]9^{y}[/tex]
[tex]mg= \sqrt{3^{x}*9^{y}} = \sqrt{3^{x}*(3^{2})^y}= \sqrt{3^{x+2y}}=9 \\ \sqrt{3^{4}}=9..deci..x+2y=4 \\ \left \{ {{x=y+1} \atop {x+2y=4}} \right. =\ \textgreater \ \left \{ {{x=y+1} \atop {y+1+2y=4}} \right. =\ \textgreater \ \left \{ {{x=y+1} \atop {3y=3}} \right. =\ \textgreater \ \left \{ {x=2{} \atop {y=1}} \right. [/tex]