Question

помогите пожалуйста,срочно нужно до завтра , номер 340 ,даю 30 баллов

Answer 1

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

$\left \{ {{y=3-x} \atop {x^2-3x+2=0}} \right. \; x_1=1,\; x_2=2\\\\b)\; \left \{ {{y=-3-x} \atop {x^2+3x+2=2}} \right. \; x_3=-1,\; x_4=-2\\\\y_1=2,\; y_2=1,\; y_3=-2,\; y_4=-1\\\\Otvet:(1,2),(2,1)$