Question 1209710
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        The answer  x = 2   in the post by  @CPhill  is  INCORRECT.



It is easy to check by substituting  x = 2  into the original equation.


You will get then  in the left side   4^(1/sqrt(2)) + 16^(1/sqrt(2)) = 9.768137  (approximately),


while the right side is   64^(1/sqrt(2)) = 18.9305.



The correct  &nbsp;<U>ANSWER</U>  &nbsp;is &nbsp;&nbsp;x = 8.299240147  (approximately).


Then  left side is  &nbsp;4^(1/sqrt(8.299240147)) + 16^(1/sqrt(8.299240147)) = 4.236067978,


the same as the right side  &nbsp;64^(1/sqrt(8.299240147)) = 4.236067978.



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For visual check, &nbsp;look at the plots of functions in the left and the right sides 
of the original equations under the link


<A HREF=https://www.desmos.com/calculator/q2kpqo337o>https://www.desmos.com/calculator/q2kpqo337o</A>


https://www.desmos.com/calculator/q2kpqo337o



Click at the intersection point to see the coordinates of this point.