`((5.624)^(3) + (4.376)^(3))/(5.624 xx 5.624 - (5.624 xx 4.376) + 4.376 xx 4.376)` is equal to

Options

A. 10
B. 1.248
C. 20.44
D. 1

Answer

To solve the expression \(\frac{(5.624)^3 + (4.376)^3}{(5.624)^2 - (5.624 \times 4.376) + (4.376)^2}\), we can use the identity for the sum of cubes and the formula for the square of a binomial.

### Step-by-step Solution:

1. **Identify the terms**:
Let \(a = 5.624\) and \(b = 4.376\). We need to evaluate the expression \(\frac{a^3 + b^3}{a^2 - ab + b^2}\).

2. **Apply the sum of cubes formula**:
The sum of cubes can be expressed as:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Therefore, we can rewrite the numerator:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]

3. **Substitute into the expression**:
Now, substituting this into our expression gives:
\[ \frac{(a + b)(a^2 - ab + b^2)}{a^2 - ab + b^2} \]

4. **Cancel out the common term**:
The \(a^2 - ab + b^2\) terms in the numerator and denominator cancel out (as long as \(a^2 - ab + b^2 \neq 0\)):
\[ a + b \]

5. **Calculate \(a + b\)**:
Now we just need to calculate \(a + b\):
\[ a + b = 5.624 + 4.376 = 10 \]

### Final Answer:
Thus, the value of the entire expression is:
\[ \boxed{10} \]