When the natural number n was increased by 1, its square increased by 1001. find n

Let n^2 = x

Thus,

(n + 1)^2 = (x + 1001)

(n + 1)^2 - 1001 = x

substitute x with n^2, getting:

(n + 1)^2 - 1001 = n^2

(n^2 + 2n + 1) - 1001 = n^2

n^2 - n^2 + 2n = 1001 - 1

2n = 1000

n = 500

x = 3 ± √(5+y)