Find-the-solution-xa-1-x-1-x-a-x-2a-a-1-0-1-and-also-find-when-a-is-not-given-

Question Number 101243 by Dwaipayan Shikari last updated on 01/Jul/20

Find the solution

{xa}^{\frac{1}{x}} + \frac{1}{x} a^{x} = 2 a a \in {- 1, 0, 1} a n d a l s o f i n d w h e n a i s n o t g i v e n

Commented by mr W last updated on 01/Jul/20

f o r a > 0 :

x = 1 i s t h e o n l y s o l u t i o n .

Commented by mr W last updated on 01/Jul/20

a = - 1 :

x {(- 1)}^{\frac{1}{x}} + \frac{{(- 1)}^{x}}{x} = - 2

\Rightarrow x = 1

a = 0 :

\Rightarrow x \in R - {0}

a = 1 :

x + \frac{1}{x} = 2

\Rightarrow x = 1

Commented by Dwaipayan Shikari last updated on 01/Jul/20

Y o u a r e r i g h t s i r . C a n y o u f i n d w h e n a i s n o t g i v e n