Quadratic Equation

To solve the equation: , let's follow these steps.

First, let and . We know from the problem statement that .

Notice that because if you multiply by , you get 1:

.

This implies .

Thus, we have:

Multiply throughout by to clear the fraction:

Rearrange this into a standard quadratic equation:

Use the quadratic formula where , , and :

This gives or .

Now, leads to implying .

Equating both conditions:

and

Multiply the two equations to verify identity:

, thus verified.

The ratio is required:

or leading to .

Therefore, the correct answer is .