What is the value of `[(7.9)^(3)+(2.4)^(3)[div[(7.9)^(2)-7.9xx2.4+(2.4)^(2)]`?

Options

A. `11.4`
B. `13.1`
C. `10.3`
D. `12.7`

Answer

To solve the problem, we need to evaluate the expression:

\[ \frac{(7.9)^3 + (2.4)^3}{(7.9)^2 - 7.9 \cdot 2.4 + (2.4)^2} \]

### Step 1: Identify the formulas
We recognize that the numerator can be expressed using the formula for the sum of cubes:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
where \( a = 7.9 \) and \( b = 2.4 \).

### Step 2: Calculate \( a + b \)
First, calculate \( a + b \):
\[ 7.9 + 2.4 = 10.3 \]

### Step 3: Calculate \( a^2 \), \( b^2 \), and \( ab \)
Next, we need to calculate \( a^2 \), \( b^2 \), and \( ab \):
\[ a^2 = (7.9)^2 = 62.41 \]
\[ b^2 = (2.4)^2 = 5.76 \]
\[ ab = 7.9 \cdot 2.4 = 18.96 \]

### Step 4: Substitute into the formula for \( a^2 - ab + b^2 \)
Now substitute these values into \( a^2 - ab + b^2 \):
\[ a^2 - ab + b^2 = 62.41 - 18.96 + 5.76 = 49.21 \]

### Step 5: Substitute into the numerator
Now, substituting back into the numerator:
\[ (7.9)^3 + (2.4)^3 = (7.9 + 2.4)((7.9)^2 - 7.9 \cdot 2.4 + (2.4)^2) = 10.3 \cdot 49.21 \]

### Step 6: Simplify the denominator
The denominator is already in the form of \( a^2 - ab + b^2 \):
\[ (7.9)^2 - 7.9 \cdot 2.4 + (2.4)^2 = 49.21 \]

### Step 7: Final calculation
Now we can simplify the entire expression:
\[ \frac{(7.9)^3 + (2.4)^3}{(7.9)^2 - 7.9 \cdot 2.4 + (2.4)^2} = \frac{10.3 \cdot 49.21}{49.21} \]
The \( 49.21 \) cancels out:
\[ = 10.3 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{10.3} \]