Question

ОЧЕНЬ СРОЧНО!ПОМОГИТЕ)Решите логарифмическую систему уравнений на фото

Answer 1

ОДЗ: x>0 и у>0

$left { {{log_3(x+2y)=1} atop {lgx+lgy=0}} right. textless = textgreater left { {{x+2y=3} atop {lg(xy)=0}} right. textless = textgreater left { {{x+2y=3} atop {xy=10^0} right. textless = textgreater left { {{x=3-2y} atop {(3-2y)y=1}} right. \ \ (3-2y)y=1 \ 3y-2y^2=1 \ 2y^2-3y+1=0 \ \ y_1=1 \ y_2=0.5 \ \ x_1=3-2y_1=3-2*1=1 \ x_2=3-2y_2=3-2*0.5=2 \ \ OTBET: (1;1); (2;0.5)$