Question 1020933
The answer is 4.

To see why, 
{{{3^(2x)+3^(-2x) = 14}}} <==> {{{3^(2x)+1/3^(2x) = 14}}} 
<==> {{{3^(4x) + 1 = 14*3^(2x)}}}
<==> {{{3^(4x) - 14*3^(2x)+1 = 0}}}
By the quadratic formula, we then get 

{{{3^(2x) = (14+-sqrt(192))/2}}}

<==>{{{3^(2x) = 7+-sqrt(48)}}} ==> {{{3^x = sqrt(7+-sqrt(48))}}}
(Note that these two values are inverses of each other, so that {{{3^x+3^(-x)}}} will have only one value, regardless whether we choose {{{3^x = sqrt(7+sqrt(48))}}} or {{{3^x = sqrt(7-sqrt(48))}}}.)

==>{{{3^x+3^(-x) = sqrt(7+-sqrt(48)) + 1/sqrt(7+-sqrt(48)) =  highlight(4) }}}