Fill in the blanks with three distinct positive integers.

1/___ + 1/___ + 1/___ = \frac{13}{12}

AnswerscorrectIy Oct 11, 2024

#2**+2 **

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!

server Oct 11, 2024