A triangle has three sides of the following side lengths: 7, 10, and \(x^2\). What are all of the positive integer values of such that the triangle exists? Separate your answers using commas and express them in increasing order.
Well, it two sides of a triangle are 7 and 10, the third side must be more than 3 (10 - 7)
and, at the same time, must be less than 17 (7 + 10)
So, you are looking for values of x such that: 3 < x2 < 17.
You'll need to list all the values of x that solve that inequality.