+859 Fill in the blanks with three distinct positive integers.
1/___ + 1/___ + 1/___ = \frac{13}{12}
+35 Lets express this as normal notation:
(sorry I don't use Latex)
1/x + 1/y + 1/z = 13/12
Wait! We know what 1/x + 1/y + 1/z is ! We just express both as a common fraction (by expressing them as a common denominator)!
(1/x + 1/y + 1/z) = (x + y) + xyz/xyz
So now:
(x + y + xyz/)xyz = 13/12
x + y +z= 13, and xyz = 12
Two equations, three variables isn't possible to solve, so we can only test numbers :(, luckily, the problem says only three distinct positive integers!
After some simple testing, we should get that only 1, 4, and 8 work.
I hope it helps, and of course, your welcome!
