3 variable equations

Dec 2015
1,084
169
Earth
Solve for positive integers : \(\displaystyle x+y+z=xyz\) .:cool:
Method required !
 
Jun 2019
493
262
USA
Wait, did my post not post? Grrr.

Let x <= y <= z.
x+y+z<=3z, thus xy<=3, thus x<=sqrt(3), thus x=1.
1+1+z=z doesn't work, so y=2 or y=3.

Yada yada, something about the Jackson 5, and there's your answer!

(Engineering method: Had MATLAB probe [1,100]^3, found 6 answers. Bada bing, bada boom!)
 
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