$$x^4+ 6x^3+13x^2+13x-1=\textrm{perfect square}$$ I don't know how to approach this. I have tried to factor this but was unable to, and equating it to squares of numbers is a tedious process, and I am not sure how to solve this problem.
By the way, this question is from Elementary Algebra by Hall and Knight, Exercise XXX b question 15.
Hint:
Can you show that $(x^2+3x+2)^2<x^4+6x^3+13x^2+13x-1<(x^2+3x+3)^2$ for $x>5$?
(A suggestion in this direction was provided by player3236 in a comment.)