Задания в вкл............

$\left \{ {{x+y=6} \atop {log_{ \sqrt{2}}x+log_{ \sqrt{2}}y=6}} \right.$

$\left \{ {{x+y=6} \atop {log_{ \sqrt{2}}(x*y)=6}} \right.$

$\left \{ {{x+y=6} \atop {x*y=2^{6* \frac{1}{2}}}} \right.$

$\left \{ {{x+y=6} \atop {x*y=2^{3}} \right.$

$\left \{ {{x=6-y} \atop {(6-y)*y=8} \right.$

$\left \{ {{x=6-y} \atop {6y-y^{2}-8=0} \right.$

$\left \{ {{x=6-y} \atop {y^{2}-6y+8=0, D=36-4*8=4} \right.$

$\left \{ {{x=6-y} \atop {y_{1}=2, y_{2}=4} \right.$

$\left \{ {{x_{1}=4} \atop {y_{1}=2} \right.$

$\left \{ {{x_{2}=2} \atop {y_{2}=4} \right.$

Ответ: (2;4), (4;2)