Question

Решите иррациональное уравнение:
√ x2−4 x+3=√1−x

Answer 1

$\sqrt{x^2-4x+3}=\sqrt{1-x}\ \ ,\\\\ODZ:\ \left\{\begin{array}{l}x^2-4x+3\geq 0\\1-x\geq 0\end{array}\right\ ,\ \ \left\{\begin{array}{l}x\leq 1\ \ ili\ \ x\geq 3\\x\leq 1\end{array}\right\ \ \Rightarrow \ \ \ x\leq 1\\\\\\x^2-4x+3=1-x\\\\x^2-3x+2=0\\\\Teorema\ Vieta\, :\ \ x_1=1\ ,\ x_2=2\notin ODZ\\\\Otvet:\ \ x=1\ .$