What is the value of `((1.1)^(3)+(0.7)^(3))/((1.1)^(2)-1.1xx0.7+(0.7)^(2))` ?

Options

A. `0.4`
B. `0.7`
C. `1.1`
D. `1.8`

Answer

To solve the expression \(\frac{(1.1)^3 + (0.7)^3}{(1.1)^2 - 1.1 \times 0.7 + (0.7)^2}\), we can use the formulas for cubes and squares.

### Step 1: Identify A and B
Let \(A = 1.1\) and \(B = 0.7\).

### Step 2: Calculate \(A^3 + B^3\)
Using the formula for the sum of cubes:
\[ A^3 + B^3 = (A + B)(A^2 - AB + B^2) \]
First, calculate \(A + B\):
\[ A + B = 1.1 + 0.7 = 1.8 \]

Next, calculate \(A^2\), \(B^2\), and \(AB\):
\[ A^2 = (1.1)^2 = 1.21 \]
\[ B^2 = (0.7)^2 = 0.49 \]
\[ AB = 1.1 \times 0.7 = 0.77 \]

Now, substitute these values into \(A^2 - AB + B^2\):
\[ A^2 - AB + B^2 = 1.21 - 0.77 + 0.49 = 1.21 - 0.77 + 0.49 = 0.93 \]

Thus,
\[ A^3 + B^3 = (1.8)(0.93) = 1.674 \]

### Step 3: Calculate the denominator
Now, calculate the denominator:
\[ A^2 - AB + B^2 = 1.21 - 0.77 + 0.49 = 0.93 \]

### Step 4: Substitute into the expression
Now substitute back into the original expression:
\[ \frac{(1.1)^3 + (0.7)^3}{(1.1)^2 - 1.1 \times 0.7 + (0.7)^2} = \frac{1.674}{0.93} \]

### Step 5: Calculate the final value
Now perform the division:
\[ \frac{1.674}{0.93} \approx 1.8 \]

### Final Answer
The value of the expression is approximately \(1.8\).

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