Question

решите систему
3^x + 3^y= 12
x+y= 3

Answer 1

x=3-y;
$3^{3-y}+ 3^{y}=(1/ 3^{y-3})+ 3^{y}=(1/ 3^{y}/ 3^{3} ) + 3^{y}= (3^{3}/ 3^{y})+ 3^{y}=12;$
$3^{y}= t$
27/t  + t = 12
$t^{2}-12t+27=0;D=144-108=36;x_{1,2}=(12+-6)/2; x_{1}=9;$$x_{2}=3$;
$3^{y}=3 <=> 3^{y}= 3^{1} => y_{1}=1$;
$3^{x}+3=12; 3^{x}=9; x_{1}=2;$
$3^{y}=9 <=> 3^{y}= 3^{2} =>y_{2}=2$;
$3^{x}+9=12; 3^{x}=3;x_{2}=1;$
Ответ:$x_{1}=2;y_{1}=1;x_{2}=1;y_{2}=2;$

Answer 2

спасибо большое0