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Let's name the first number x and the next number x + 1. So,
x^2 - (x + 1)^2
= x^2 - (x^2 + 2x + 1)
= x^2 - x^2 - 2x - 1
= - 2x - 1
= -(2x + 1)
Thus we can say that, the difference between the squares of two consecutive numbers is equal to the opposite of their sum (means it is their sum, but as a negative number).
Let's do some examples:
2, 3; 2 + 3 = 5
2^2 - 3^2 = 4 - 9 = -5 ( 5 and -5 are opposite numbers, and 5 is the sum of 2 and 3)
13, 14; 13 + 14 = 27
13^2 - 14^2 = 169 - 196 = -27 (27 and -27 are opposite numbers, and 27 is the sum of 13 and 14)
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Which two consecutive whole numbers does the square root of fifty five lie between?
Just check the squares of a few whole numbers. If 55 is between two of those squares, then its square root is also between the corresponding square roots.
What are the two consecutive numbers whose squares add to 365?
The numbers are 13 and 14.
The sum of the squares of two consecutive odd integers is 34 what are the numbers?
3 and 5
The sum of the squares of two consecutive odd numbers is 130 what are the numbers?
7 and 9 72+92 = 130
The sum of the squares of two consecutive positive even integers is 340Find the integers?
The numbers are 12 and 14.
