If the expression `x + 809436 xx 809438` be a perfect square, then the value of x is

Options

A. 0
B. 1
C. 809436
D. 809438

Answer

To solve the problem, we need to determine the value of \( x \) such that the expression \( x + 809436 \times 809438 \) is a perfect square.

### Step-by-Step Solution:

1. **Understand the Expression**:
The expression we have is:
\[ x + 809436 \times 809438 \]
We can rewrite \( 809438 \) as \( 809436 + 2 \). Thus, we can express the multiplication as:
\[ 809436 \times (809436 + 2) \]

2. **Use the Algebraic Identity**:
We can use the identity \( a(a + b) = a^2 + ab \). Here, let \( a = 809436 \) and \( b = 2 \):
\[ 809436 \times 809438 = 809436^2 + 809436 \times 2 \]

3. **Calculate the Expression**:
Substitute back into the expression:
\[ x + 809436^2 + 2 \times 809436 \]
This simplifies to:
\[ x + 809436^2 + 1618872 \]

4. **Set Up for Perfect Square**:
For the entire expression to be a perfect square, we can set:
\[ x + 809436^2 + 1618872 = k^2 \]
for some integer \( k \).

5. **Rearranging the Equation**:
Rearranging gives:
\[ x = k^2 - (809436^2 + 1618872) \]

6. **Finding a Suitable \( k \)**:
We need to find \( k \) such that \( k^2 \) is a perfect square. To simplify our calculations, we can consider \( k = 809436 + 1 \) (since we are looking for a perfect square close to \( 809436^2 \)):
\[ k = 809437 \]
Thus, calculate:
\[ k^2 = 809437^2 \]

7. **Calculate \( k^2 \)**:
Now calculate \( 809437^2 \):
\[ 809437^2 = 809436^2 + 2 \times 809436 + 1 \]

8. **Substituting Back**:
Substitute back into the equation for \( x \):
\[ x = (809436^2 + 2 \times 809436 + 1) - (809436^2 + 1618872) \]
Simplifying gives:
\[ x = 2 \times 809436 + 1 - 1618872 \]
\[ x = 1618872 + 1 - 1618872 \]
\[ x = 1 \]

### Conclusion:
The value of \( x \) that makes the expression a perfect square is:
\[ \boxed{1} \]