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Question:

If n is a positive integer, then (√3+1)²ⁿ - (√3-1)²ⁿ is:

an odd positive integer

an even positive integer

a rational number other than positive integers

an irrational number

Solution:

Given,(√3+1)2n−(√3𕒵)2nThe above question can be broken into[((√3+1)2)n−((√3𕒵)2)n]=2n[(2+√3)n−(2−√3)n]