The difference between the squares of two consecutive numbers is 141. Find the numbers

The difference between the squares of two consecutive numbers is 141. Find the numbers

Take two consecutive numbers:
n- 1 and n

Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is:
2n - 1 = d

Proof of this:
n^2- (n - 1)^2 = d
n^2 - (n^2 - 2n + 1) = d
n^2 - n^2 + 2n - 1 = d
2n - 1 = d

Given d = 141, we have
2n - 1 = 141

Add 1 to each side:
2n = 142

Divide each side by 2:
2n/2 = 142/2
n = 71

Therefore, n - 1 = 70

Our two consecutive numbers are (70, 71)

Check your work
70^2 = 4900
71^2 = 5041

Difference = 5041 - 4900
Difference = 141