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Consider the sequence \((u_n)\) defined by \(u_0 = 4\) and \(u_{n+1} = \dfrac{u_n + 8}{u_n + 3}\).We assume that \((u_n)\) converges to a real number \(\ell\).
  1. State the equation that \(\ell\) must satisfy.
  2. Solve this equation to find the value of \(\ell\) (noting that \(u_n > 0\) for all \(n\)).

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