SOLUTION: 1. If the product of two consecutive odd integers is 783, what is the sum of their squares? 2. The difference between the squares of two consecutive positive integers is 2013. Wha

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: 1. If the product of two consecutive odd integers is 783, what is the sum of their squares? 2. The difference between the squares of two consecutive positive integers is 2013. Wha      Log On


   

Question 758601: 1. If the product of two consecutive odd integers is 783, what is the sum of their squares?
2. The difference between the squares of two consecutive positive integers is 2013. What is the larger integer?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. If the product of two consecutive odd integers is 783, what is the sum of their squares?
1st: 2x-1
2nd: 2x+1
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Equation:
4x^2-1 = 783
4x^2 = 784
x^2 = 196
x = 14
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1st: 2x-1 = 27
2nd: 2x+1 = 29
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2. The difference between the squares of two consecutive positive integers is 2013. What is the larger integer?
1st: x
2nd: x+1
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Equation:
(x+1)^2 - x^2 = 2013
2x+1 = 2013
2x = 2012
x = 1006
------
x+1 = 1007
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. If the product of two consecutive odd integers is 783, what is the sum of their squares?
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sqrt(783) =~ 28, the center
--> 27 & 29
27^2 + 29^2 = 1570
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2. The difference between the squares of two consecutive positive integers is 2013. What is the larger integer?
--------
(n+1)^2 - n^2 = 2013
n = 1006