perplexus.info :: Just Math : 3 unknowns

3 unknowns (Posted on 2023-09-18)

The set of integers {x,y,z} complies with the following set of equations:

x+y+xy=17
x+z+xz=35
y+z+yz=71

Evaluate {x,y,z}.

No Solution Yet Submitted by Ady TZIDON

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re: Puzzle Solution

| Comment 2 of 4 |

(In reply to Puzzle Solution by K Sengupta)

A^2*B^2*C^2 = 18*36*72 = 18^2* 2*72 = 18^2*12^2

=> ABC = 18*12 = 216

Since you took a square root and the problem domain is all integers, there is also the branch ABC=-216.

From there A=-6 -> x=-7; B=-3 -> y=-4; and C=-12 -> z=-13.

Then a second solution is found (x,y,z)=(-7,-4,-13).

Posted by Brian Smith on 2023-09-18 11:50:58

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