Question

plz solve this.. answer is root 2 plz give solution ,spams will be reported ​

Answer 1

Given :

• A^( 1/A ) = B^( 1/B ) = C^( 1/C )

• A^( BC ) + B^( AC ) + C^( AB ) = 729

To find :

Value of A^( 1/A )

Solution :

Let A^( 1/A ) = B^( 1/B ) = C^( 1/C ) = p

Taking power ABC

⇒ { A^( 1/A ) }^( ABC ) = { B^( 1/B ) }^( ABC ) = { C^( 1/C ) }^( ABC ) = p^( ABC )

⇒ A^( BC ) = B^( AC ) = C^( AB ) = p^( ABC )

Now, substituting the values in the equation A^( BC ) + B^( AC ) + C^( AB ) = 729

⇒ p^( ABC ) + p^( ABC ) + p^( ABC ) = 729

⇒ 3p^( ABC ) = 729

⇒ p^( ABC ) = 729 / 3 = 243

⇒ p^( ABC ) = 243

⇒ p = 243^( 1/ABC )

⇒ A^( 1/A ) = 243^( 1/ABC )

Therefore the value of A^( 1/A ) is 243^( 1/ABC )

Answer 2

$\bold\green{Step\: By\: Step \:Explanation}$

According to the question we have given :-

$\implies \sf{ {A}^{ \frac{1}{A} } = {B}^{ \frac{1}{B} } = {C}^{ \frac{1}{C} } } \\ \\ \implies \sf{ {A}^{ BC } = {B}^{ AC} = {C}^{ AB} = 729}$

So, we have to find the value of :-

$\implies \sf{ {A}^{ \frac{1}{A} } }$

So, let us assumed that :-

$\implies \sf{ {A}^{ \frac{1}{A} } = {B}^{ \frac{1}{B} } = {C}^{ \frac{1}{C} } \: = P }$

Now , by taking power ABC

$\implies \sf{ ({A}^{ \frac{1}{A} })^{ABC} = ({B}^{ \frac{1}{B} })^{ABC} = ({C}^{ \frac{1}{C} })^{ABC} \: = P^{ABC} }$

$\implies \sf{ ({A}^{ })^{BC} = ({B}^{ })^{AC} = ({C}^{ })^{AB} \: = P^{ABC} }$

Now , we subsitute the value in equation :-

$\implies \sf \green{ {A}^{ BC } + {B}^{ AC} + {C}^{ AB} = 729}$

$\implies \sf{P^{ABC} + \: P^{ABC} + \: P^{ABC} = 729 } \\ \implies \sf{3P ^{ABC} = 729}$

$\implies \sf{P^{ABC} = \cancel\frac{729}{3} = 243 }$

$\implies \sf{P ^{ABC} = 243}$

$\implies \sf{P = 243^{ \frac{1}{ABC} }}$

$\implies \sf{A ^{ \frac{1}{A} } = 243^{ \frac{1}{ABC} }}$

$\sf{Hence\:the\: required\: value\:of\:A ^{ \frac{1}{A} } \: is\: 243^{ \frac{1}{ABC} }}$