Solve for x,y and z;If

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xy+x+y=23
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yz+y+z=31
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zx+z+x=47
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Input your answer as the sum of positive values of x,y,z.

The answer is 15.

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Re-writing these equations as (x+1)(y+1)=24, (y+1)(z+1)=32 and (z+1)(x+1)=48, then multiplying out and taking square-root gives (x+1)(y+1)(z+1)=192, which on dividing out above equations one by one gives (z+1) = 8, (x+1)=6 and (y+1)=4. Consequently, x, y and z are 5, 3 and 7, respectively, and their sum is 15.