If $(x + 1) (x + 2) (x + 3) (x + k) + 1$ is a perfect square then the value of k is

4

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5

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6

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7

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Solution

The correct option is A $4$
$(x + 1) (x + 2) (x + 3) (x + k) + 1 = n^{2}$
$N o w, n^{2} - 1 = f (x) - 1$
$(n + 1) (n - 1) = (x + 1) (x + 2) (x + 3) (x + k)$
Accordingly factors should must be resolved in consecutive sets $,$
Hence $,$ $k = 4$ yields the consecutive set of factors of $24$ simultaneously, which further results is $n^{2} = 25$
Hence,
Option $(A)$ is correct answer.

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