There is no solution but we can show why there is no solution.



Square both sides:



Simplify:



Cube both sides:



Simplify:







We try 1 to see if it is a solution:

1 | 1 -1  2 -1
  |    1  0  2 
    1  0  2  1

1 is not a solution. However, since all numbers on the 
bottom row of the synthetic division are non-negative, 
1 is an upper bound for the solutions.  So any solutions 
are therefore less than 1.  However any solution less than
1 when substituted into the original equation, which is:  



will yield a negative number on the left side.  However
the right side is non-negative because the square root
radical cannot be a negative number.  Therefore there
can be no solution.

We can check that conclusion graphically, heuristically.

Below is the graph of



From which we can see there is no solution for y=0 since

the entire graph is below the x-axis.



Edwin