What is the value of `[(6.5)^(3)+(4.7)^(3)]div[(6.5)^(2)-6.5xx4.7+(4.7)^(2)]?`

Options

A. a. 11.2
B. b. 13.5
C. c. 12.7
D. d. 13.2

Answer

To solve the expression \(\frac{(6.5)^3 + (4.7)^3}{(6.5)^2 - 6.5 \times 4.7 + (4.7)^2}\), we can use the algebraic identity for the sum of cubes and the formula for the denominator.

### Step-by-Step Solution:

1. **Identify A and B**:
Let \( A = 6.5 \) and \( B = 4.7 \).

2. **Use 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:
\[ (6.5)^3 + (4.7)^3 = (6.5 + 4.7)((6.5)^2 - (6.5)(4.7) + (4.7)^2) \]

3. **Simplify the Denominator**:
The denominator is already in the form \( A^2 - AB + B^2 \):
\[ (6.5)^2 - (6.5)(4.7) + (4.7)^2 \]

4. **Substituting into the Expression**:
Substitute the numerator and denominator into the expression:
\[ \frac{(6.5 + 4.7)((6.5)^2 - (6.5)(4.7) + (4.7)^2)}{(6.5)^2 - (6.5)(4.7) + (4.7)^2} \]

5. **Cancel the Common Terms**:
The common term \((6.5)^2 - (6.5)(4.7) + (4.7)^2\) cancels out:
\[ = 6.5 + 4.7 \]

6. **Calculate the Final Value**:
Now, calculate \( 6.5 + 4.7 \):
\[ 6.5 + 4.7 = 11.2 \]

### Final Answer:
The value of the expression is \( 11.2 \).

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