Question

If $a^{x} = (x + y + z)^{y},a^{y} = (x + y + z)^{z}$, $a^{z} = (x + y + z)^{x},$ then

• A. $x = y = z = a/3$
• B. $x + y + z = a/3$
• C. $x + y + z = 0$
• D. None of these

Answer 1

Answer: (A)

$x = y = z = a/3$

Answer 2

$a^{x}.a^{y}.a^{z} = (x + y + z)^{y + z + x}$

$\Rightarrow a^{x + y + z} = (x + y + z)^{x + y + z} \Rightarrow$ $x + y + z = a$

Now, $a^{x} = (x + y + z)^{y} = a^{y} \Rightarrow$ $x = y$, similarly $y = z$

$\therefore x = y = z = \frac{a}{3}$.