You also could have looked at the answers I posted on Friday, which were incorrect (I edited my post on Saturday)
Thank you
So now I'm relieved. That was a really nice problem.
Well, it seems that I used a bit more algebra in my solution than you did, but the equation I obtained was far too complex for me to solve it or find its derivative without a little help of a computer
I'm posting my solution below, have a look if you wish.