+128474 xy + x + y = 23
yz + y + z = 31
zx + z + x = 47
Probably a better way to do this....but, anyway
xy + y = 23 -x zx + z = 47 - x
y ( x + 1) = 23 -x z ( x + 1) = 47-x
y = (23 -x) / (x + 1) z = (47 - x) / ( x + 1)
yz + y + z = 31
( 23-x) /( x + 1) ( 47 - x)/ (x + 1) + (23- x)/(x+1) + (47 -x) /(x + 1) = 31
Multiply through by (x + 1)^2
(23 - x) ( 47 - x) + (23 - x)(x + 1) + (47 - x) ( x + 1) =31 ( x + 1)^2
x^2 - 70x + 1081 -x^2 +22x + 23 -x^2 + 46x + 47 = 31x^2 + 62x + 31 simplfify as
32x^2 + 64x -1120 = 0 divide through by 32
x^2 + 2x - 35 = 0 factor
(x + 7) ( x -5) = 0
Set both factors to 0 , solve for x
x = -7 y = (23 - -7)/( -7 + 1) = 30/-6 = -5 z = (47 - -7 ) /(-7 + 1) = 54/ -6 = -9
x = 5 y = ( 23 - 5) / (5 + 1) = 18/6 = 3 z = (47 - 5)/(5 + 1) = 42/6 =7
So
{ x, y , z} = { -7, -5, -9) or { 5, 3, 7}
