The sides of a triangle are `x^2+x+1, 2x+1 and x^2-1.` Prove that the greatest angle is `120^0`

Explanation

To prove that the greatest angle of the triangle with sides \( a = x^2 + x + 1 \), \( b = 2x + 1 \), and \( c = x^2 - 1 \) is \( 120^\circ \), we will follow these steps:

### Step 1: Verify that all sides are positive
We need to ensure that \( a \), \( b \), and \( c \) are all positive for the triangle inequality to hold.

1. **For side \( a \)**:
\[
a = x^2 + x + 1
...