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sum of squares of 3 different positive integers

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by smitathakur64 » Tue Dec 27, 2011 7:54 pm
Question: 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?
1)17
2)16
3)15
4)14
5)13

I tried to solve it by trial and error method. Tried all the combinations of squares, till I got to the right answer(1,5,7). Is this the right way of doing it or is there any better and quicker way.
The answer is 13.

Thanks
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by Anurag@Gurome » Tue Dec 27, 2011 8:27 pm
smitathakur64 wrote:Question: 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?
1)17
2)16
3)15
4)14
5)13

I tried to solve it by trial and error method. Tried all the combinations of squares, till I got to the right answer(1,5,7). Is this the right way of doing it or is there any better and quicker way.
The answer is 13.

Thanks
Trial and error is the fastest way to answer this question.
The perfect squares under 75 are: 1, 4, 9, 16, 25, 36, 49, and 64
Now we have to find 3 different numbers from the above integers, which add to 75, 1 + 25 + 49 = 75
So, their roots are 1, 5, and 7, which add to 13.
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