Verified answer

Ответ:

[tex]\left(\frac{1}{2};\frac{3}{4} \right)\\\\\\xy=\frac{3}{8}[/tex]

Объяснение:

[tex]\begin{cases}3^{x-2y}=\frac{1}{3}\\3^x+3^{2y}=4\sqrt 3\end{cases}\\\\\begin{cases}3^{x-2y}=3^{-1}\\3^x+3^{2y}=4\sqrt 3\end{cases}\\\\\begin{cases}x-2y=-1\\3^x+3^{2y}=4\sqrt 3\end{cases}\\\\\begin{cases}x=2y-1\\3^x+3^{2y}=4\sqrt 3\end{cases}\\\\\begin{cases}x=2y-1\\3^{2y-1}+3^{2y}=4\sqrt 3\end{cases}[/tex]

[tex]3^{2y-1}+3^{2y}=4\sqrt 3\\\\3^{2y}\cdot 3^{-1}+3^{2y}=4\sqrt 3\\\\3^{2y}\cdot (3^{-1}+1)=4\sqrt 3\\\\3^{2y}\cdot (\frac{1}{3}+1)=4\sqrt 3\\\\\frac{4}{3}\cdot 3^{2y}=4\sqrt 3\ \ \ |:\frac{4}{3}\\\\3^{2y}=4\sqrt 3\cdot \frac{3}{4}\\\\3^{2y}=3\sqrt 3\\\\3^{2y}=3\cdot 3^{\frac{1}{2}}\\\\3^{2y}=3^{\frac{3}{2}}2y=\frac{3}{2}\ \ \ |:2\\\\y=\frac{3}{4}\\\\x=2y-1=2\cdot \frac{3}{4}-1=\frac{3}{2}-1=\frac{1}{2}\\\\\left(\frac{1}{2};\frac{3}{4} \right)\\\\\\xy=\frac{1}{2}\cdot \frac{3}{4}=\frac{3}{8}[/tex]