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Consider the sequence \((u_n)\) defined by \(u_0 = 1\) and \(u_{n+1} = \sqrt{u_n + 6}\).
Suppose that \((u_n)\) converges to a real number \(\ell\).
  1. Justify that \(\ell\) must be a solution to the equation \(x = \sqrt{x+6}\).
  2. Solve this equation and determine the value of \(\ell\).

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