Задача 64242 Решите систему уравнений......
Условие
Решение
[m]\left\{\begin {matrix}x ≥ 0\\y ≥ 0\\xy>0\end {matrix}\right.[/m]
⇒ x>0; y>0
[m]\left\{\begin {matrix}2^{\sqrt{x}+\sqrt{y}}=512\\lg\sqrt{xy}=1+lg2\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}2^{\sqrt{x}+\sqrt{y}}=2^{9}\\lg\sqrt{xy}=lg10+lg2\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}2^{\sqrt{x}+\sqrt{y}}=2^{9}\\lg\sqrt{xy}=lg20\end {matrix}\right.[/m] ⇒
[m]\left\{\begin {matrix}\sqrt{x}+\sqrt{y}=9\\\sqrt{xy}=20\end {matrix}\right.[/m] ⇒
[m]\left\{\begin {matrix}\sqrt{x}=4\\\sqrt{y}=5\end {matrix}\right.[/m] ИЛИ [m]\left\{\begin {matrix}\sqrt{x}=5\\\sqrt{y}=4\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x=16\\y=25\end {matrix}\right.[/m] ИЛИ [m]\left\{\begin {matrix}x=25\\y=16\end {matrix}\right.[/m]
О т в е т. (16;25); (25;16)