If G and L are the greatest and least values of the expression `(x^(2)-x+1)/(x^(2)+x+1), x epsilon R` respectively then
`G` and `L` are the roots of the equation

Options

A. `3x^(2)-10x+3=0`
B. `4x^(2)-17x+4=0`
C. `x^(2)-7x+10=0`
D. `x^(2)-5x+6=0`

Explanation

To solve the problem, we need to find the greatest and least values of the expression \( f(x) = \frac{x^2 - x + 1}{x^2 + x + 1} \) and then form the quadratic equation whose roots are these values.

### Step-by-step Solution:

1. **Define the Function**:
Let \( f(x) = \frac{x^2 - x + 1}{x^2 + x + 1} \).

2. **Find Critical Points**:
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