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sum of the squares

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sum of the squares

by sanju09 » Fri Apr 10, 2009 5:40 am
The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A. 17
B. 16
C. 15
D. 14
E. 13



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by dmateer25 » Fri Apr 10, 2009 5:45 am
7^2 = 49
5^2 = 25
1^1 = 1

49 + 25 + 1 = 75

7 + 5 + 1 = 13

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by kapsii » Fri Apr 10, 2009 5:56 am
Not an elegant way to do it, but the only one I could think of:

Start writing the squares of integers... (keeping in mind that you need their sum to be 75 which is 25 * 3, i.e. 25 + 25 + 25)
1,4,9,16,25,36,49,64,81

while writing them down I stopped after 49, as I had found which three perfect squares can make 75, 1 + 25 + 49.

hence answer has to be: 1 + 5 + 7 = 13.
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