Find \(x\)

Calculus Level pending

A recurrent relation is defined as follows:

  • \(A_{0} =A_{1} =A_{2} = 890 \)
  • \(A_{n} =(A_{n-1} + A_{n-2} + A_{n-3})^{\frac{1}{x}}\) for \(n>2\)
  • \(\displaystyle \lim_{n \to \infty} A_{n} = \sqrt[4]{3} \)

Find \(x\).

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