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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.
What are 2 consecutive numbers whose squares differ by 17?
The difference between the squares of two consecutive integers j and j+1 is |2j+1|. There are therefore two such pairs where this quantity is 17:-9 and -88 and 9
What are three consecutive square numbers?
There are no three consecutive numbers that are squares. Otherwise, there are an infinite sets of squares of three consecutive numbers: for example, {1,4,9}, or {4,9,16} or {576, 625, 676}
Difference between the sum of the squares and the square of the sums of n numbers?
Difference between the sum of the squares and the square of the sums of n numbers?Read more:Difference_between_the_sum_of_the_squares_and_the_square_of_the_sums_of_n_numbers
What are the consecutive square numbers that add up to 77?
16,25,36 add to 77. They are the squares of consecutive numbers 4,5,6
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.
The difference of the squares of two consecutive odd numbers is 48What are the odd numbers?
The numbers are (x) and (x+2).Their squares are (x)2 and (x+2)2, or (x2) and (x2 + 4x + 4).The difference between the squares is (x2 + 4x + 4) - (x2) = 4x + 4 = 484x + 4 = 48x + 1 = 12x = 11 and (x + 2) = 13======================Check:112 = 121132 = 169169 - 121 = 48 yay!
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 positive numbers is 61. What are the smaller numbers?
5
What 2 consecutive numbers whose squares differ by 17?
8
The sum of the squares of two consecutive positive numbers is 61?
5
What are two consecutive numbers whose squares differ by 31?
15 and 16
What are two consecutive numbers whose squares diffee by 35?
17 and 18
