Show that
I was thinking along the lines of dividing both sides by , rearranging and comparing the cubes of both sides but doesnt seem to work.
There is probably a simpler proof, but here is what i suggest:
We go to a proof by contradiction. Assume that is valid:
We raise both sides to cube:
By binomial expansion we have:
By extracting as common factor the term:
we do have:
But we know that
So by substituting we have:
Or
By raising again to cube we have that:
which is false.