Question

помогите решить систему
log0,5х+log0,5у=-1
х-2у=3

Answer 1

I hope this helps you

Answer 2

ОДЗ x > 0, y > 0
$left { {{log0,5_x + log0,5_y = -1} atop {x-2y=3}} right. = textgreater left { {{log0,5_(x*y) = log0,5_2} atop {x-2y=3}} right. = textgreater left { {{x*y=2} atop {x-2y=3}} right.$

$left { {{(3+2y)*y=2} atop {x=3+2y}} right. = textgreater left { {{3y+2y^2-2=0} atop {x=3+2y}} right. = textgreater left { {{2y^2+3y-2=0} atop {x=3+2y}} right.$

2y^2+3y-2=0
D=25
y1 = -2
y2 = 0,5

x1 = 3 + 2* (-2) = -1
x2 = 3 + 2*(0,5)= 4

(-1;-2) не подходят по одз

Ответ: (4;0,5)