What is the positive real root of the equation $x^4-x-1=0$? I tried to solve the question on the graph and got two roots also I used Newton Raphson rule but a general proof is required. Any kind suggestions will be appreciated.
Also the root = √√(1+√√(1+√√(1+√√(1+... hence when I solved this on my calculator I got the root but I don't know whether there is a closed form for it or not

According to wolfram alpha, exact form of this solutions are

The former is positive solution.
