How can I prove 1 2 1

Curious evidence

If this first proof was not enough for you, please also have a look at this second proof. It is known that:

Now replace 1 with a, 2 with b and 3 with c:

Again, multiply by (a-b) ...

... releases the brackets ...

... and arranges according to parts with a or b:

Now we add (c / 2)2 (square addition):

Based on the 2nd binomial formula, this results in:

If you take the root, you get:

If we add (c / 2) we get:

Since a = 1 and b = 2, we get: