# A new problem based on ye olde problem of yore

I tried to make up my own problem along the lines of this problem, but wanting it to be slightly different.

Let $x^4=7+4\sqrt{3}$. Show that $x+\frac{1}{x}=\sqrt{6}$ exactly.

Coming up with your own problems is so much harder than solving problems.

(If you need help, see the solution to the problem linked above. The general method I used for solving this problem is the same method I used for creating this problem.)