Determine the value of 'x', if `x = ((943 + 864)^(2) - (943 - 864)^(2))/((1886 xx 1728))`

Options

A. 1
B. 4
C. 79
D. 1789

Answer

To determine the value of \( x \) given the expression

\[ x = \frac{(943 + 864)^2 - (943 - 864)^2}{1886 \times 1728} \]

we can simplify the expression step by step.

### Step 1: Identify \( a \) and \( b \)
Let \( a = 943 \) and \( b = 864 \).

### Step 2: Apply the difference of squares formula
The expression in the numerator can be simplified using the difference of squares formula:

\[ A^2 - B^2 = (A - B)(A + B) \]

where \( A = 943 + 864 \) and \( B = 943 - 864 \).

### Step 3: Calculate \( A \) and \( B \)
Calculate \( A \) and \( B \):
- \( A = 943 + 864 = 1807 \)
- \( B = 943 - 864 = 79 \)

### Step 4: Use the difference of squares
Now apply the difference of squares:

\[ (943 + 864)^2 - (943 - 864)^2 = (A - B)(A + B) = (1807 - 79)(1807 + 79) \]

### Step 5: Calculate \( A - B \) and \( A + B \)
Calculate \( A - B \) and \( A + B \):
- \( A - B = 1807 - 79 = 1728 \)
- \( A + B = 1807 + 79 = 1886 \)

### Step 6: Substitute back into the expression
Now substitute back into the expression:

\[ x = \frac{(1728)(1886)}{1886 \times 1728} \]

### Step 7: Simplify the expression
The \( 1886 \times 1728 \) in the numerator and denominator cancels out:

\[ x = 1 \]

### Final Answer
Thus, the value of \( x \) is

\[ \boxed{1} \]