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by bstalling » Mon Feb 02, 2009 7:26 pm
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

This should be easy but I don't see it...
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by truplayer256 » Mon Feb 02, 2009 7:47 pm
I honestly don't know a better way to solve this problem other than using guess and check.

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

The first thing I did was I thought of the lowest perfect square less than 75, which would be 64. So, 75-64=11. Are there any two numbers whose squares add up to 11? the answer to that would be no. The next lowest perfect square after 64 is 49, so, 75-49=26. Are there any two numbers whose squares add up to 26? Yes, 1 and 5. Now we have our x and y:

x=5,y=1,z=sqrt(49)=7

5+1+7=13 E
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by bstalling » Mon Feb 02, 2009 8:06 pm
OA is E
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