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What is the largest 3 digit number that is the sum of the squares of two consecutive even natural numbers?
Suppose the smaller of the two even natural numbers is 2x. Then the other one is 2x + 2
The sum of their squares is (2x)2 + (2x + 2)2 = 4x2 + 4x2 + 8x + 4 = 8x2 + 8x + 4
You want 8x2 + 8x + 4 < 1000
that is 8x2 + 8x - 996 < 0
or 2x2 + 2x - 249 < 0
x < {-2 + sqrt[22 - 4*2*(-249)]}/(2*2)
= {-2 + sqrt[4 + 1992]}/(4)
= {-2 + sqrt[1996]}/(4)
= {-2 + 44.68}/4
= 42.68/4
= 21.34
So x = 20
Then, the sum is 202 + 222 = 400 + 484 = 884
What else can I help you with?
What is the largest three digit number that is the sum of the squares of two consecutive even natural numbers?
202 + 222 = 400 + 484 = 884
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}
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.
The sum of the squares of two consecutive positive numbers is 41 What is the smaller number?
4
What is the largest three digit number that is the sum of the squares of two consecutive even natural numbers?
202 + 222 = 400 + 484 = 884
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}
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
Perfect squares?
Natural numbers which are the scales of some natural numbers are perfect squares
The sum of the squares of two consecutive positive numbers is 61. What are the smaller numbers?
5
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?
5
What 2 consecutive numbers whose squares differ by 17?
8
What are two consecutive numbers whose squares differ by 125?
62 and 63
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
What is The sum of the squares of two consecutive positive numbers is 61 what is the smaller number?
The numbers are 5 and 6.
