Question

Решите систему уравнений и найти ОДЗ log2(x-y)=3 ; 4^log2(корень x+y)=10

Answer 1

$left { {{log_2(x-y)=3} atop {4^{log_2sqrt{x+y}}=10}} right.$
ОДЗ:$x-y textgreater 0;x textgreater y$
$sqrt{x+y} textgreater 0;x+y textgreater 0;x textgreater -y$

$left { {{log_2(x-y)=log_2 8} atop {2^{2log_2sqrt{x+y}}=10}} right.$
$left { {{(x-y)=8} atop {2^{log_2(x+y)}=10}} right.$
$left { {{x-y=8} atop {x+y=10}} right.$
$left { {{2x=18} atop {x+y=10}} right.$
$left { {{x=9} atop {9+y=10}} right.$
$left { {{x=9} atop {y=1}} right.$