<s>[INST] Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$ 
The real numbers $p$, $q$, $r$, $s$ satisfy 
  $$p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$$ 
  Find the value of $s$.

I don't even know how to start. Thanks!
 [/INST] Let $t = \sqrt{p+q+r-s}$, the equation is equivalent to
$$\begin{align} & p^2+q^2+r^2+1 = (p+q+r-t^2) + t\\
\iff & \left(p - \frac12\right)^2+\left(q - \frac12\right)^2+\left(r - \frac12\right)^2 + \left(t - \frac12\right)^2 = 0\\
\implies & p = q = r = t = \frac12\\
\implies & s = p + q + r - t^2 = \frac54\end{align}$$
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