Question

50 БАЛЛОВ!!! Помогите решить, пожалуйста, с подробным решением

Answer 1

1)
$left { {{log_2 (x+y)=3} atop {log_{15} x=1-log_{15} y}} right.$
ОДЗ: $x textgreater 0; y textgreater 0; x textgreater -y$

$left { {{log_2 (x+y)=log_2 2^3} atop {log_{15} x=log_{15} 15-log_{15} y}} right.$
$left { {{log_2 (x+y)=log_2 8} atop {log_{15} x=log_{15} frac{15}{y}}} right.$
$left { {{x+y= 8} atop {x=frac{15}{y}}} right.$
$left { {{frac{15}{y}+y= 8} atop {x=frac{15}{y}}} right.$
$left { {{frac{15+y^2-8y}{y}= 0} atop {x=frac{15}{y}}} right.$
$left { {{y^2-8y+15= 0} atop {x=frac{15}{y}}} right.$
$left { {{(y-3)(y-5)= 0} atop {x=frac{15}{y}}} right.$

$left { {{y=3} atop {x=frac{15}{y}}} right.$
$left { {{y=3} atop {x=frac{15}{3}=5}} right.$

$left { {{y=5} atop {x=frac{15}{5}=3}} right.$
Два решения - (3,5) и (5,3)
2)
$left { {{log_3 (xy)=2+log_3 2} atop {log_3 (x+y)=2}} right.$
ОДЗ:$xy textgreater 0; x textgreater -y$

$left { {{log_3 (xy)=log_3 9+log_3 2} atop {log_3 (x+y)=log_3 9}} right.$
$left { {{log_3 (xy)=log_3 18} atop {log_3 (x+y)=log_3 9}} right.$
$left { {{xy=18} atop {x+y= 9}} right.$
$left { {{xy=18} atop {x= 9-y}} right.$
$left { {{(9-y)y=18} atop {x= 9-y}} right.$
$left { {{9y-y^2-18=0} atop {x= 9-y}} right.$
$left { {{(3-y)(y-6)=0} atop {x= 9-y}} right.$

$left { {{y=3} atop {x= 9-y}} right.$
$left { {{y=3} atop {x= 9-3=6}} right.$

$left { {{y=6} atop {x= 9-y}} right.$
$left { {{y=6} atop {x= 9-6=3}} right.$

Два решения - (6,3) и (3,6)

Answer 2

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