數學知識交流---繁分數求值(3)

Let the expression = a.
Let the recurring denominator = y
so sqrt 13 + ( - 13 + sqrt 13)/y = a ............(1)
Add sqrt 13 to both sides of (1), we get
2 sqrt 13 + ( - 13 + sqrt 13)/y = a + sqrt 23
but 2 sqrt 13 + ( - 13 + sqrt 13)/y is in fact equal to y because y is recurring infinitely, that is y = a + sqrt 13 .............(2)
Sub (2) into (1)
sqrt 13 + ( - 13 + sqrt 13)/(a + sqrt 13) = a
sqrt 13(a + sqrt 13) + (- 13 + sqrt 13) = a(a + sqrt 13)
a sqrt 13 + 13 - 13 + sqrt 13 = a^2 + a sqrt 13
sqrt 13 = a^2
so a = 13^(1/4) = the expression.

i calculated to a = 13^(1/4) or -13^(1/4)

but i cant find which one is the correct ans