Refer to question posted on blog of Mar 13 2018, reproduced here for your convenience. Compare your solution with the one given here:
Show that the following expression: remains constant in the interval . Find this constant value.
Let y equal the given expression for x in the prescribed interval. Then, taking cube of both sides, we write
The only real value of , a constant. The roots of the quadratic equation for are complex. It is easy to check that for both and 1.
Alternately, derive the square roots of the expression within the radical; you can use the method of undetermined coefficients for this.