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75 = x^2 + y^2 + z^2

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abehrman
 Post subject: 75 = x^2 + y^2 + z^2
 Post Posted: Mon Jan 25, 2010 11:45 pm 
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Course Students


Posts: 6
75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?

Is there a way that this can be done except by trial and error? Are there certain numbers that I should start with?
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nishant_gourav
 Post subject: Re: 75 = x^2 + y^2 + z^2
 Post Posted: Tue Jan 26, 2010 3:03 pm 
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Students


Posts: 1
7,5,1
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shilpman
 Post subject: Re: 75 = x^2 + y^2 + z^2
 Post Posted: Thu Jan 28, 2010 5:05 pm 
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Posts: 1
the-number-75-can-be-written-as-the-sum-of-the-squares-t2175.html?hilit=75%20numbers
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debasish.banerjee
 Post subject: Re: 75 = x^2 + y^2 + z^2
 Post Posted: Wed Feb 03, 2010 3:02 pm 
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Course Students


Posts: 1
can someone pls. explain how 7,5,1 was chosen?
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kevinmarmstrong
 Post subject: Re: 75 = x^2 + y^2 + z^2
 Post Posted: Fri Feb 05, 2010 5:24 pm 
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Posts: 28
list the perfect squares less than 75:

1 4 9 16 25 36 49 64

Could the sum involve 64? The sum of the other two squares would have to be 11: impossible.

How about 49? The sum of the other two squares would have to be 26= 25 + 1

Thus 75= 7^2 + 5^2 +1^2
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RonPurewal
 Post subject: Re: 75 = x^2 + y^2 + z^2
 Post Posted: Thu Mar 04, 2010 10:40 am 
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ManhattanGMAT Staff


Posts: 7146
Quote:
Is there a way that this can be done except by trial and error?


unfortunately... not really.

takeaway:
do not expect a "textbook solution" for every problem.
if a problem has a SMALL NUMBER OF POSSIBILITIES, you can expect to have to try those possibilities, one by one.

Quote:
Are there certain numbers that I should start with?


see here:
post7260.html#p7260
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