Question

РЕШИТЕ СИСТЕМУ УРАВНЕНИЙ!

Answer 1

$\left \{ {{log_2 x+log_2 y=log_2 6} \atop {x^2+y^2=13}} \right; \\ x>0; y>0;\\ \left \{ {{log_2 (xy)=log_2 6} \atop {x^2+y^2=13}} \right; \\ \left \{ {{xy=6} \atop {x^2+y^2=13}} \right; \\ x=\frac{6}{y};\\ (\frac{6}{y})^2+y^2=13;\\ y^4-13y^2+36=0;\\ (y^2-4)(y^2-9)=0;\\ (y-2)(y+2)(y+3)(y-3)=0; \\ y_1=2; x_1=\frac{6}{2}=3; y_2=-2<0; y_3=-3<0; y_4=3; x_4=\frac{6}{3}=2$

значит решения (2;3) и (3;2)