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Ratio of 5th term from the beginning to 5th term from the end in (2^(1/4) + 1/3^(1/4))^n: find n, then a term

The same question, asked 2 times: 29 Jul 2022*, 6 Apr 2023. Every wording below, oldest first.

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  1. Question 1

    29 Jul 2022

    85
    Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of (24+134)n\left( \sqrt[4]{2}+\frac{1}{\sqrt[4]{3}} \right)^{n}, in the increasing powers of 134\frac{1}{\sqrt[4]{3}} be 64:1\sqrt[4]{6}:1. If the sixth term from the beginning is α34\frac{\alpha}{\sqrt[4]{3}}, then α\alpha is equal to

  2. Question 2

    6 Apr 2023

    64
    If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of (24+134)n\left( \sqrt[4]{2}+\frac{1}{\sqrt[4]{3}} \right)^{n} is 6:1\sqrt{6}:1, then the third term from the beginning is:

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