[tex] \left \{ {{lg(x^2+y^2)=1+lg8} \atop {lg(x+y)-lg(x-y)=lg3}} ight. [/tex]

ОДЗ x+y>0 U x-y>0{lg(x²+y²)=lg80{lg[(x+y)/(x-y)]=lg3{x²+y²=80{[(x+y)/(x-y)]=3x+y=3x-3y3x-x=y+3y2x=4yx=2y4y²+y²=805y²=80y²=16y1=-4        x1=-8  не удов усл,т.к. -4-8=-12<0 и -8+4=-4<0y2=4          x2=8Ответ (8;4)