Question

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.

Answer 1

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