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The problem asks to write a quadratic equation with given roots and a leading coefficient \( a = 1 \). The roots are:

1. \( 2 - \sqrt{3} \)
2. \( \frac{1}{2 - \sqrt{3}} \)

### Step 1: Rationalizing the second root
We need to simplify \( \frac{1}{2 - \sqrt{3}} \) by rationalizing the denominator:

\[
\frac{1}{2 - \sqrt{3}} \cdot \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = \frac{2 + \sqrt{3}}{(2 - \sqrt{3})(2 + \sqrt{3})}
\]

Using the difference of squares:

\[
(2 - \sqrt{3})(2 + \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1
\]

Thus:

\[
\frac{1}{2 - \sqrt{3}} = 2 + \sqrt{3}
\]

### Step 2: Using the sum and product of roots to form the quadratic equation
Let the roots be \( r_1 = 2 - \sqrt{3} \) and \( r_2 = 2 + \sqrt{3} \). The quadratic equation can be formed as:

\[
x^2 - (r_1 + r_2)x + r_1r_2 = 0
\]

1. **Sum of the roots:**

\[
r_1 + r_2 = (2 - \sqrt{3}) + (2 + \sqrt{3}) = 4
\]

2. **Product of the roots:**

\[
r_1r_2 = (2 - \sqrt{3})(2 + \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1
\]

### Step 3: Forming the quadratic equation
Now we substitute the sum and product into the standard quadratic form:

\[
x^2 - 4x + 1 = 0
\]

Thus, the quadratic equation is:

\[
\boxed{x^2 - 4x + 1 = 0}
\]

Let me know if you'd like more details or have questions! Here are 5 related questions for further practice:

1. How do you form a quadratic equation if the roots are complex numbers?
2. What is the process of completing the square for solving quadratic equations?
3. Can you apply the quadratic formula to verify the solution?
4. What are the steps for factoring a quadratic equation with integer roots?
5. How do you solve a quadratic equation graphically?

**Tip:** Always simplify roots or expressions before substituting them into equations to avoid errors.

Write a quadratic equation with the following roots: 2 - √3 and 1 / (2 - √3), with the leading coefficient a = 1.

This solution explains how to write a quadratic equation with roots involving radicals, 2 - √3 and its reciprocal. It covers concepts of rationalizing denominators and the sum and product of roots. Ideal for students in Grades 10-12.

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