Question

If $x^x.y^y.z^z=x^y.y^z.z^x$ 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 ?

• A. xyz=27
• B. xyz=1728
• C. x+y+z=32
• D. x+y+z=12

Answer 1

The correct option is C x+y+z=32

$\begin{array}{c}{x}^x.y^y.z^z=x^y.y^z.z^x\\ \therefore x=y\\ y=z\\ z=x\\ xyz=27\end{array}$

$forx=y=z=3$

Hence,

Option $C$ is correct answer as it gives a value of $\frac{32}{3}=10.667$

which isnt an integer