0,y>0\\\\ \left \{ {{x^2+y^2=5} \atop {\log_2(xy)=\log_22}} \right. \; \left \{ {{x^2+y^2=5} \atop {xy=2}} \right. \; \left \{ {{x^2+y^2=5} \atop {2xy=4}} \right. \\\\ \left \{ {{x^2+2xy+y^2=5+4} \atop {xy=2}} \right. \left \{ {{(x+y)^2=9} \atop {xy=2}} \right. \; \left \{ {{x+y=\pm 3} \atop {xy=2}} \right. \; \; \to \\\\a)\; \left \{ {{x+y=3} \atop {xy=2}} \right. \; \left \{ {{y=3-x} \atop {x(3-x)=2}} \right. \; " alt=" \left \{ {{x^2+y^2=5} \atop {\log_2x+\log_2y=1}} \right. ODZ:x>0,y>0\\\\ \left \{ {{x^2+y^2=5} \atop {\log_2(xy)=\log_22}} \right. \; \left \{ {{x^2+y^2=5} \atop {xy=2}} \right. \; \left \{ {{x^2+y^2=5} \atop {2xy=4}} \right. \\\\ \left \{ {{x^2+2xy+y^2=5+4} \atop {xy=2}} \right. \left \{ {{(x+y)^2=9} \atop {xy=2}} \right. \; \left \{ {{x+y=\pm 3} \atop {xy=2}} \right. \; \; \to \\\\a)\; \left \{ {{x+y=3} \atop {xy=2}} \right. \; \left \{ {{y=3-x} \atop {x(3-x)=2}} \right. \; " align="absmiddle" class="latex-formula">
