Question

The number 2017 can be expressed as the difference of the squares of two consecutive whole numbers. What is the sum of these two numbers?

Answer 1

Let x be the first number

X + 1 be the second number

So

(x+1)^2 – x^2 = 2017

X^2 + 2x +1 – x^2 = 2017

2x + 1 = 2017

2x = 2017 – 1

2x = 2016

X = 1008

X + 1 = 1009

Sum = 1008 + 1009 = 2017