Question

If $x^y=y^z=z^x$ and $x z=y^2$, then which of the following is correct?

• A. $z=\frac{2 x y}{x+y}$
• B. $y=\frac{x-z}{x+z}$
• C. $x=\frac{y-z}{y z}$
• D. $x y z=\frac{x-z+y}{x+z-y}$

Answer 1

Answer: (A)

(i) Consider $x^y=y^z=z^x=k$.
(ii) Express $x z=y^2$ in terms of $k$