+479 Suppose that x,y,z are positive integers satisfying x is less than or equal to y is less than or equal to z, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of z?
+118667 Suppose that x,y,z are positive integers satisfying x is less than or equal to y is less than or equal to z, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of z?
I just made a possible list and then cancelled the ones that didn't work. I was left with 3 possible triads
You know \(x\le y\le z\qquad \text{Where that are all positive integers}\)
and you know
\(xyz=2(x+y+z)\)
the smallest the RHS can be is 6 and the biggest is 54
So the product of x, y and z is between 6 and 54
Now I just listed all the possibilities for the triads that multiply to between 6 and 54 and then cancelled them out if they did not fit the equality.
Give it a go.
the smallest one is
1,1,6
then
1,1,7
etc.
Try doing it yourself.
