Question

If $A^{1/A}=B^{1/B}=C^{1/C},A^{BC}+B^{AC}+C^{AB}=729$
Which of the following equals $A^{1/A}$

Answer 1

$a^{\frac{1}{a}}=b^{\frac{1}{b}}=c^{\frac{1}{c}}$

$\Rightarrow a^{\frac{abc}{a}}=b^{\frac{abc}{b}}=c^{\frac{abc}{c}}$

$\Rightarrow a^{bc}=b^{ac}=c^{ab}$

from given,

$a^{bc}+b^{ac}+c^{ab}=729$

$\Rightarrow 3a^{bc}=729$

$\therefore a^{bc}=243=3^5$

$\Rightarrow a=3,bc=5$

$\therefore a^{\frac{1}{a}}=3^{\frac{1}{3}}$