If-x-x-y-y-z-z-x-y-y-z-z-x-x-z-y-x-z-y-such-that-x-y-and-z-are-positive-integers-greater-than-1-then-which-of-the-following-cannot-be-true-for-any-of-the-possible-value-of-x-y-and-z-

Question Number 22472 by Tinkutara last updated on 18/Oct/17

If x^{x} \cdot y^{y} \cdot z^{z} = x^{y} \cdot y^{z} \cdot z^{x} = x^{z} \cdot y^{x} \cdot z^{y} such

that x, y and z are positive integers

greater than 1, then which of the

following cannot be true for any of the

possible value of x, y and z ?

(1) x y z = 27

(2) x y z = 1728

(3) x + y + z = 32

(4) x + y + z = 12