`(8.73xx8.73xx8.73+4.27xx4.27xx4.27)/(8.73xx8.73-8.73xx4.27+4.27xx4.27)=`

Options

A. 11
B. 12
C. 13
D. 10

Answer

To solve the expression \((8.73 \times 8.73 \times 8.73 + 4.27 \times 4.27 \times 4.27) / (8.73 \times 8.73 - 8.73 \times 4.27 + 4.27 \times 4.27)\), we can use the algebraic identity for the sum and difference of cubes.

### Step-by-Step Solution:

1. **Identify the Terms**:
- Let \( A = 8.73 \) and \( B = 4.27 \).
- The expression can be rewritten as:
\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

2. **Use the Identity**:
- We know from algebra that:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
- Therefore, we can substitute this into our expression:
\[ \frac{(A + B)(A^2 - AB + B^2)}{A^2 - AB + B^2} \]

3. **Simplify the Expression**:
- Since \( A^2 - AB + B^2 \) is in both the numerator and denominator, we can cancel it out (as long as it is not zero):
\[ A + B \]

4. **Calculate \( A + B \)**:
- Now, substitute back the values of \( A \) and \( B \):
\[ A + B = 8.73 + 4.27 = 13 \]

5. **Final Answer**:
- Therefore, the value of the given expression is:
\[ \boxed{13} \]