Another algebraic identity guaranteed to make you smarter.

If x can be expressed as (y+z) or (y-z),

Such that y²-z²=1 or y²-z²=(-1),

Then x²+1/x²=2(y²+z²).

Proof:

Case 1: x=(y+z) and y²-z²=1

Case 2: x=(y-z) and y²-z²=1

Case 3: x=(y+z) and y²-z²= (-1)

Case 4: x=(y-z) and y²-z²=(-1)

How to use the identity? Two examples below:

Use them and show how smart you are!!!