Notice that for 2 numbers a and b, (a+1)(b+1)=ab+a+b+1 This is very similar to the equations above, so we can rewrite the equations like this:
(x+1)(y+1)−1=19→(x+1)(y+1)=20(y+1)(z+1)−1=29→(y+1)(z+1)=30(z+1)(x+1)−1=5→(z+1)(x+1)=6
Let us replace (x+1) with a, (y+1) with b, and (z+1) with c, so it is easier to solve:
ab=20bc=30ca=6
Multiply all the equations and then take the square root:
a2b2c2=3600abc=60
Now, to solve for a, b, and c, just divide abc by one of the equations of ab, bc, or ca:
a=abcbc=2b=abcac=10c=abcab=3
Now, subtract each of a, b, and c by 1 to solve for x, y and z, respectively:
x=1y=9z=2
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