A triangle has three sides of the following side lengths: 7, 10, and \(x^2\). What are all of the positive integer values of x such that the triangle exists? Separate your answers using commas and express them in increasing order.

\(\text{The key thing is that the sum of the length of any two sides is greater than the length of the third side}\\ 7+10 > x^2\\ 17>x^2\\~\\ x^2+7>10\\ x^2 > 3\\ \text{integer values of $x$ are $2,3,4$}\)