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What is the largest 3 digit number that is the sum of the squares of two consecutive even natural numbers?
Wiki User
∙ 12y ago
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
Wiki User
∙ 12y ago
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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 is two consecutive numbers whose squares differ by 25?
12 and 13
What are two consecutive positive even numbers the sum of whose squares is 340?
The numbers are 12 and 14.
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}
Perfect squares?
Natural numbers which are the scales of some natural numbers are perfect squares
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
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
What are two consecutive numbers whose squares differ by 125?
62 and 63
What is two consecutive numbers whose squares differ by 25?
12 and 13
