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The difference between the squares of two consecutive numbers is the sum of those two numbers.
For example:
2 squared is 4.
3 squared is 9.
9-4=5
2+3=5
This is for a very simple reason:
To go from 2x2 or '2 lots of two' to '3 lots of two' (3x2) we must add another two.
3 lots of two equals 2 lots of three. To get to three lots of two we need another three. We have added two then three, or 2+3.
You can also apply this rule two numbers further apart, but to discover their squares' difference you must add them together and multiply by their difference
EG. 2 squared is 4
4 squared is 16
16-4= 12
(2+4)x2=12
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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
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!
The sum of the squares of two consecutive positive numbers is 61. What are the smaller numbers?
5
What are two consecutive positive even numbers the sum of whose squares is 340?
The numbers are 12 and 14.
