We will need two formulas:
and
Let
Then we are given that
We need to show that .
Expand what we are given by first formula:
or
Since then
Now, equation can be rewritten as
Or
For simplicity, make substitution
Then we have that
There is only one real solution t=2, so
Finally,
That's all.
You're given
Let . Cubing both sides of this equation yields
, substitute with .
. Here, it helps to know that is. However, we know that . Squaring both sides of this equation yields
. Substitute into the previous equation to obtain
. Here it is evident that is a root (the other two roots are non-real). Hence we are done.