It is give positive number `x,y,z` which satisfied that `x^2+y^2=z^2`. Prove that: `xyz` is divided by `x+y+z`.

 It is give positive number `x,y,z` which satisfied that `x^2+y^2=z^2`. Prove that: `xyz` is divided by `x+y+z`.

Solution

From the following hypothesis: `x^2+y^2=z^2` we can rewrite such as: `x^2+y^2+2xy=z^2+2xy` 

                                            `(x+y)^2=z^2+2xy`

                                            `2xy=(x+y+z)(x+y-z)`

We can see that: `(x+y+z)` or `(x+y-z)` is divided by 2 which `(x+y-z)` gives remain same to `(x+y+z)` then `(x+y-z)` is dived by 2 exactly.
Let, `x+y-z=2k` then `xy=k(x+y+z)`then `xyz` is dived by `x+y+z`.

Solution by: Thin Sokkean