Question

Решите систему уравнений:

$\left \{ {{\sqrt{x} +\sqrt{y} =5} \atop {x-y=10}} \right.$

Answer 1

$\begin{cases}\sqrt x+\sqrt y=5\\x-y=10\end{cases}\Longleftrightarrow\quad\begin{cases}x=10+y\\\sqrt{10+y}+\sqrt{y}=5\end{cases}$

$\begin{array}{lcl}\sqrt{10+y}+\sqrt y=5\\\\\sqrt{10+y}=5-\sqrt{y}\end{array}\qquad\qquad\qquad\begin{array}{lcl}x=10+y\\\\x=10+2.25=12.25\end{array}\\\\10+y=25-10\sqrt{y}+y\\\\10\sqrt{y}=15\\\\\sqrt{y}=\dfrac{15}{10}\\\\\sqrt y=1.5\\\\y=2.25$

Ответ: (12,25 ; 2,25)