The product of two consecutive positive integers is added to the larger of the two integers. Prove that the result is always a square number.

Question

Thank you for your help.

Answer 1

1st number = X.
2nd number = X+1.

(x+1) + x(x+1) = x+1 + x^2+x = x^2 + 2x + 1 = (x+1)(x+1) = (x+1)^2.