\ANG{
Berechne die L"osungsmenge:\qquad
$\D\sqrt{x+23}=\sqrt{x-1}+\sqrt{x-22}$
}
\LSG{
$x>22\quad\DANN\quad\DD=[22,+\infty[$
\begin{align}
  x+23&=x-1+x-22+2\sqrt{x^{2}-23x+22}\nonumber\\
  46-x&=2\sqrt{x^{2}-23x+22}\nonumber\\
  2116-92x+x^{2}&=4x^{2}-92x+88\nonumber\\
  x^{2}&=676\quad\DANN\quad x_{1}=26,\quad
  \left(x_{2}=-26\notin\DD\right)\nonumber
\end{align}
}
