1. 

Cube both sides:








   

There is no need to check that because we raised variables
only to an ODD power.  It is only when you raise variables
to an even power that you might get extraneous solutions.



2.  

Cross-multiply



Square both sides:











   

We must check this because we raised variables to an
EVEN power, and this may be an extraneous solution.




We need go no further because there can be no real
solution if there is a negative number under an EVEN
root, such as a square root, 4th root, 6th root, etc.

This equation has no real solution.


3. 

Raise both sides to the 4th power:











This can have no real solution.

Edwin