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April 16th, 2014, 03:41 PM   #1
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solve

x+y+z=56
(x+z)(z+y)=1568
x^2+y^2=z^2
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April 16th, 2014, 05:32 PM   #2
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Hello, mared!

Quote:
$\displaystyle \begin{array}{ccccc}x+y+z \;=\; 56 & [1] \\
(x+z)(z+y) \;=\; 1568 & [2] \\
x^2+y^2 \;=\; z^2 & [3]\end{array}$

[3] says we have a Pythagorean triple.
[1] says its sum is 56.

The answer is: $\displaystyle \:(x,y,z) \:=\:(7,24,25)\:\text{ or }\:(24,7,25)$

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