# 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.)

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

You also understand the concept, and its connections, much deeper when you create problems. I routinely ask all my students to create problems for every topic they study. It’s also empowering for them. Last but not least, planning this activity is as easy as it gets :-) You just ask people to create their own problems.