Question
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.
Thank you for your help.
Thank you for your help.
Answers
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.
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.
Related Questions
The sum of the reciprocals of three consecutive positive integers is equal to 47 divided by the prod...
For two consecutive positive even integers, the product of the smaller and twice the larger is 160....
The positive difference of the cubes of two consecutive positive integers is 111 less than five
tim...