In what way can I use the two formulas you hinted about

to show my proof?

Try this. USING THE FORMULAS, WRITE DOWN the distance between a and the arithmetic mean. What is it? Write down the distance between b and the arithmetic mean. What is it? Do you see any way to equate those two expressions?

If you do not see a way to equate them, please post your answers to the distance questions, and say what you tried. I'll bet big money you can solve this on your own after you write down the distances.

Many students think that you find the answer before writing anything down. Not at all. You START by writing down what you know, all of it, and look for connections.