![image](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Blog_3x%2Blog_3y%3D1-log_32%7D+%5Catop+%7Blog_3%28x%2By%29%3D2%7D%7D+%5Cright.+%5C%3B+%2C%5C%3B++%5Cleft+%5C%7B+%7B%7Blog_3%28xy%29%3Dlog_33-log_32%7D+%5Catop+%7Bx%2By%3D3%5E2%7D%7D+%5Cright.+%5C%3B+%2C%5C%3B++%5Cleft+%5C%7B+%7B%7Blog_3%28xy%29%3Dlog_3%5Cfrac%7B3%7D%7B2%7D%7D+%5Catop+%7Bx%2By%3D9%7D%7D+%5Cright.+%5C%5C%5C%5C+%5Cleft+%5C%7B+%7B%7Bxy%3D%5Cfrac%7B3%7D%7B2%7D%7D+%5Catop+%7By%3D9-x%7D%7D+%5Cright.+%5C%3B+%2C%5C%3B++%5Cleft+%5C%7B+%7B%7Bx%289-x%29%3D%5Cfrac%7B3%7D%7B2%7D%7D+%5Catop+%7By%3D9-x%7D%7D+%5Cright.+%5C%3B+%2C%5C%3B++%5Cleft+%5C%7B+%7B%7Bx%5E2-9x%2B%5Cfrac%7B3%7D%7B2%7D%3D0%7D+%5Catop+%7By%3D9-x%7D%7D+%5Cright.+%5C%3B+%2C%5C%3B++%5Cleft+%5C%7B+%7B%7B2x%5E2-18x%2B3%3D0%7D+%5Catop+%7By%3D9-x%7D%7D+%5Cright.+%5C%5C%5C%5C2x%5E2-18x%2B3%3D0%5C%5C%5C%5CD%2F4%3D81-6%3D75%2C%5C%5C%5C%5Cx_1%3D%5Cfrac%7B9-5%5Csqrt3%7D%7B2%7D%3E0%5C%3B+%2C)
0\; ," alt=" \left \{ {{log_3x+log_3y=1-log_32} \atop {log_3(x+y)=2}} \right. \; ,\; \left \{ {{log_3(xy)=log_33-log_32} \atop {x+y=3^2}} \right. \; ,\; \left \{ {{log_3(xy)=log_3\frac{3}{2}} \atop {x+y=9}} \right. \\\\ \left \{ {{xy=\frac{3}{2}} \atop {y=9-x}} \right. \; ,\; \left \{ {{x(9-x)=\frac{3}{2}} \atop {y=9-x}} \right. \; ,\; \left \{ {{x^2-9x+\frac{3}{2}=0} \atop {y=9-x}} \right. \; ,\; \left \{ {{2x^2-18x+3=0} \atop {y=9-x}} \right. \\\\2x^2-18x+3=0\\\\D/4=81-6=75,\\\\x_1=\frac{9-5\sqrt3}{2}>0\; ," align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B9%2B5%5Csqrt3%7D%7B2%7D%5C+%5Ctextgreater+%5C+0%5C%5C%5C%5Cy_1%3D9-x_1%3D9-%5Cfrac%7B9-5%5Csqrt3%7D%7B2%7D%3D%5Cfrac%7B9%2B5%5Csqrt3%7D%7B2%7D%5C+%5Ctextgreater+%5C+0%5C%5C%5C%5Cy_2%3D9-x_2%3D9-%5Cfrac%7B9%2B5%5Csqrt3%7D%7B2%7D%3D%5Cfrac%7B9-5%5Csqrt3%7D%7B2%7D%3E0%5C%5C%5C%5COtvet%3A%5C%3B+%5C%3B+%28%5Cfrac%7B9-5%5Csqrt3%7D%7B2%7D%3B%5Cfrac%7B9%2B5%5Csqrt3%7D%7B2%7D%29%5C%3B+%5C%3B+%3B%5C%3B+%28%5Cfrac%7B9%2B5%5Csqrt3%7D%7B2%7D%3B%5Cfrac%7B9-5%5Csqrt3%7D%7B2%7D%29.)
0\\\\Otvet:\; \; (\frac{9-5\sqrt3}{2};\frac{9+5\sqrt3}{2})\; \; ;\; (\frac{9+5\sqrt3}{2};\frac{9-5\sqrt3}{2})." alt="x_2=\frac{9+5\sqrt3}{2}\ \textgreater \ 0\\\\y_1=9-x_1=9-\frac{9-5\sqrt3}{2}=\frac{9+5\sqrt3}{2}\ \textgreater \ 0\\\\y_2=9-x_2=9-\frac{9+5\sqrt3}{2}=\frac{9-5\sqrt3}{2}>0\\\\Otvet:\; \; (\frac{9-5\sqrt3}{2};\frac{9+5\sqrt3}{2})\; \; ;\; (\frac{9+5\sqrt3}{2};\frac{9-5\sqrt3}{2})." align="absmiddle" class="latex-formula">