If `x^2 - 4x + 3 = 0`, then what is the value of `(x - 2)^2`?

Options

A. `-1`
B. `0`
C. `1`
D. `3`

Answer

To solve the equation \( x^2 - 4x + 3 = 0 \) and find the value of \( (x - 2)^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ x^2 - 4x + 3 = 0 \]

2. **Rearrange the equation:**
We can rewrite the equation to isolate the constant term:
\[ x^2 - 4x = -3 \]

3. **Complete the square:**
To complete the square, we take the coefficient of \( x \) (which is -4), divide it by 2, and square it:
\[ \left(-\frac{4}{2}\right)^2 = (-2)^2 = 4 \]
Now, we add and subtract this square inside the equation:
\[ x^2 - 4x + 4 - 4 = -3 \]
This simplifies to:
\[ (x - 2)^2 - 4 = -3 \]

4. **Isolate the squared term:**
Now, we can move -4 to the right side:
\[ (x - 2)^2 = -3 + 4 \]
Simplifying the right side gives:
\[ (x - 2)^2 = 1 \]

5. **Conclusion:**
Therefore, the value of \( (x - 2)^2 \) is:
\[ (x - 2)^2 = 1 \]

### Final Answer:
The value of \( (x - 2)^2 \) is \( 1 \).

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