\ANG{
Berechne die L"osungsmenge:\qquad
$\D\sqrt{x+314}=\sqrt{x-1}+\sqrt{x-313}$
}
\LSG{
$x>313\quad\DANN\quad\DD=[313,+\infty[$
\begin{align}
  x+314&=x-1+x-313+2\sqrt{x^{2}-314x+313}\nonumber\\
  628-x&=2\sqrt{x^{2}-314x+313}\nonumber\\
  394384-1256x+x^{2}&=4x^{2}-1256x+1252\nonumber\\
  x^{2}&=131044\quad\DANN\quad x_{1}=362,\quad
  \left(x_{2}=-362\notin\DD\right)\nonumber
\end{align}
}