Question

с иррациональными уравнениями

Answer 1

$1)\ \ \sqrt{2x+63}=x\ \ \ \Leftrightarrow \ \ \left\{\begin{array}{l}x\geq 0\\2x+63=x^2\end{array}\right\ \ \left\{\begin{array}{l}x\geq 0\\x^2-2x-63=0\end{array}\right\\\\\\\left\{\begin{array}{l}x\geq 0\\x_1=-7\ ,\ x_2=9\end{array}\right\ \ \ \ \Longrightarrow \ \ \ \underline {\ x=9\ }\geq 0$

$2)\ \ \sqrt{72-21x}=-x\ \ \ \Leftrightarrow \ \ \left\{\begin{array}{l}-x\geq 0\\72-21x=(-x)^2\end{array}\right\ \ \left\{\begin{array}{l}x\leq 0\\x^2+21x-72=0\end{array}\right\\\\\\\left\{\begin{array}{l}x\leq 0\\x_1=-24\ ,\ x_2=3\end{array}\right\ \ \ \ \Longrightarrow \ \ \ \underline{\ x=-24\ }\leq 0$