If a expression `x + 2374156 xx 2374158` is a perfect square, then find the value of x.

Options

A. 10
B. 1
C. 2374156
D. 2374158

Answer

To solve the problem, we need to determine the value of \( x \) such that the expression \( x + 2374156 \times 2374158 \) is a perfect square.

### Step-by-Step Solution:

1. **Understanding the Expression**:
We start with the expression:
\[ x + 2374156 \times 2374158 \]

2. **Using the Difference of Squares**:
Notice that \( 2374156 \times 2374158 \) can be rewritten using the difference of squares formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
Here, let \( a = 2374157 \) (the average of \( 2374156 \) and \( 2374158 \)) and \( b = 1 \). Thus, we have:
\[ 2374156 \times 2374158 = (2374157 - 1)(2374157 + 1) = 2374157^2 - 1^2 = 2374157^2 - 1 \]

3. **Substituting Back into the Expression**:
Now substitute this back into the original expression:
\[ x + (2374157^2 - 1) \]
Simplifying this gives:
\[ x + 2374157^2 - 1 \]

4. **Setting Up the Perfect Square Condition**:
For the entire expression to be a perfect square, we can set:
\[ x + 2374157^2 - 1 = k^2 \]
where \( k \) is some integer. Rearranging gives:
\[ x = k^2 - 2374157^2 + 1 \]

5. **Finding the Value of \( x \)**:
To ensure that \( x \) is a perfect square, we can set \( k = 2374157 \):
\[ x = 2374157^2 - 2374157^2 + 1 = 1 \]

6. **Conclusion**:
Therefore, the value of \( x \) that makes the expression a perfect square is:
\[ \boxed{1} \]