SOLUTION: Find x, (7 + √x)^⅓ + (7 - √x)^⅓ = 2

Your starting equation is

     +  = 2.    (1)


Let  a = ;  b = .


Raise both sides of equation (1) to degree 3.

Use

     =  + 3ab*(a+b),


     =   +  = 14,

    a + b = 2   <<<---===  given by equation,

    ab = .


You will get

     = 8.


Simplify and find x

     = ,

     = -1.


Raise both sides of the last equation to degree 3

    49 - x = -1,

    49 + 1 = x,

     x     = 50.


ANSWER.  x = 50.


CHECK.    +  = 2.414213562 + (-0.414213562) = 2.0000000