What is the value of `((6.3)^(3)+(1.1)^(3))/((6.3)^(2)-6.3xx1.1+(1.1)^(2))`

Options

A. 7.4
B. 5.2
C. 7.2
D. 6.8

Answer

To solve the expression \(\frac{(6.3)^3 + (1.1)^3}{(6.3)^2 - 6.3 \times 1.1 + (1.1)^2}\), we can use algebraic identities.

1. **Identify Variables**: Let \(A = 6.3\) and \(B = 1.1\). The expression can be rewritten as:
\[ \frac{A^3 + B^3}{A^2 - AB + B^2} \]

2. **Use the Identity for Sum of Cubes**: The formula for the sum of cubes is:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
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 the 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 \(B\):
\[ A + B = 6.3 + 1.1 = 7.4 \]

5. **Final Answer**: Therefore, the value of the expression is:
\[ \boxed{7.4} \]