Question

РЕШИТЬ системы под номером 4 и 5 . Очень подробно используя строку формул.

Answer 1

$4)\; \; \left \{ {{3^{2+log_3(2x-y)}=45} \atop {log_8(x+y)+log_8(x-y)=1}} \right. \; \left \{ {{3^2\cdot 3^{log_3(2x-y)}=45} \atop {log_8((x+y)(x-y))=1}} \right. \; \left \{ {{9\cdot (2x-y)=45} \atop {x^2-y^2=8}} \right. \\\\ \left \{ {{y=2x-5} \atop {x^2-4x^2+20x-25=8}} \right. \; \left \{ {{y=2x-5} \atop {3x^2-20x+33=0}} \right. \; \left \{ {{y_1=1\; ,\; y_2=\frac{7}{3}} \atop {x_1=3\; ,\; x_2=\frac{11}{3}}} \right. \\\\Otvet:\; (3;1)\; (\frac{11}{3};\frac{7}{3})\; ;\; (x\ \textgreater \ y,\; x\ \textgreater \ -y,\; 2x\ \textgreater \ y)$

$5)\; \left \{ {{log_2x+log_2y=2} \atop {x-4y=15}} \right. \; \; ODZ:\; x\ \textgreater \ 0,\; y\ \textgreater \ 0 \\\\\left \{ {{log_2(xy)=2} \atop {x=4y+15}} \right. \; \left \{ {{xy=4} \atop {x=4y+15}} \right. \; \left \{ {{4y^2+15y-4=0} \atop {x=4y+15}} \right. \; \left \{ {{y_1=-4,\; y_2=0,25} \atop {x_1=-1,\; x_2=16}} \right. \\\\Otvet:\; (16;\; 0,25).$