SOLUTION: The square of the sum of two successive even numbers is 100. Calculate the value of the numbers

Question 1137356: The square of the sum of two successive even numbers is 100. Calculate the value of the numbers
Found 2 solutions by Alan3354, Olasko:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
6 & 8 if you mean the sum of the squares.
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If not,
(n + n+2)^2 = 100
n + n+2 = 10 or -10
---> 4 & 6 or -6 & -4

Answer by Olasko(10) (Show Source): You can put this solution on YOUR website!
Let the nos be n and n+2 (difference of even numbers)
n + n + 2 = 2n + 2
( 2n + 2 )^2 = 100
4n^2 + 8n + 4 = 100
n^2 + 2n + 1 = 25
n^2 + 2n - 24 = 0
solve to obtain
n = 4 or -6
overlook the negative one
hence, the numbers are 4 and 6
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