Question

There are three different positive integers whose reciprocals add up to 1. What is the product of those three integers?

Answer 1

\[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\]
where \(x,y,z\) are the three positive integers.
\[\begin{align*}\frac{yz}{xyz}+\frac{xz}{xyz}+\frac{xy}{xyz}&=1\\\\
yz+xz+xy&=xyz
\end{align*}\]
The first solution that comes to mind is \(x=2\), \(y=3\) and \(z=6\), which gives \(xyz=36\).

Not sure if there are more possibilities for \(x,y,z\)...

Answer 2

OH MY GOSH
thanks so much it's right your my hero!!!!!!!!!!!!!!!

Answer 3

thanks:)

Answer 4

yw