Question

Помогите пожалуйста решить

Answer 1

$left { {{log_2 x+ frac{1}{2}log_2 frac{1}{y}=4} atop {xy=2}} right.$
ОДЗ:$x textgreater 0;y neq 0;y textgreater 0$
$left { {{log_2 frac{x}{ sqrt{y} }=log_2 16} atop {xy=2}} right.$
$left { {{frac{x}{ sqrt{y} }= 16} atop {xy=2}} right.$
$left { {{x= 16sqrt{y}} atop {xy=2}} right.$
$left { {{x= 16sqrt{y}} atop {16sqrt{y}*y=2}} right.$
$left { {{x= 16sqrt{y}} atop {y^{ frac{3}{2} }= frac{1}{8} }} right.$
$left { {{x= 16sqrt{y}} atop {y^{ frac{3}{2} }=2^{-3} }} right.$
$left { {{x= 16sqrt{y}} atop {y=(2^{-3})^{ frac{2}{3} } }} right.$
$left { {{x= 16sqrt{y}} atop {y=2^{-2} }} right.$
$left { {{x= 16sqrt{y}} atop {y= frac{1}{4} }} right.$
$left { {{x= 16sqrt{ frac{1}{4} }} atop {y= frac{1}{4} }} right.$
$left { {{x= 16* frac{1}{2} } atop {y= frac{1}{4} }} right.$
$left { {{x= 8} atop {y= frac{1}{4} }} right.$