# Another algebraic identity guaranteed to make you smarter.

2 min readMay 21, 2020

If ** x** can be expressed as

**or**

*(y+z)***,**

*(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!!!