Consider the equation an^2 = 182 where a is any number between 2 and 5 and n is a positive interger. What are the possible values of n?

The possible values of n are 7, 8, 9

The given equation is:

an²  =  182

Make n the subject of the formula:

Let us consider the minimum and maximum values of a:

when a = 2

When a = 5

We can conclude that 6.03 < n < 9.54

Since n is an integer, the possible values of n are 7, 8, 9

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Step-by-step explanation:

an² = 182

When a = 2, n² = 182/2 = 91, n = 9.539...

When a = 5, n² = 182/5 = 36.4, n = 6.033...

Since 2 <= a <= 5, we have 6.033 <= n <= 9.539.

Therefore our possible values of n are 7, 8 and 9.