# Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (4√2 + 1/4√3)^n is √6:1.

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Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of (4√2 + 1/4√3)is 6:1.

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Solution:

In the expansion, ,

Fifth term from the beginning

Fifth term from the end

Therefore, it is evident that in the expansion of, the fifth term from the beginning is and the fifth term from the end is.

It is given that the ratio of the fifth term from the beginning to the fifth term from the end is √6:1. Therefore, from (1) and (2), we obtain

Thus, the value of n is 10.