What is the value of `[(1.7)^(3) - (1. 2)^(3)]//[(1 . 7)^(2) + (1. 7 xx 1. 2) + (1.2)^(2)]`?

Options

A. `0.5`
B. `2.9`
C. `1.9`
D. `0.7`

Answer

To solve the expression \(\frac{(1.7)^3 - (1.2)^3}{(1.7)^2 + (1.7 \times 1.2) + (1.2)^2}\), we can follow these steps:

### Step 1: Calculate \((1.7)^3\) and \((1.2)^3\)
- First, we calculate \((1.7)^3\):
\[ (1.7)^3 = 1.7 \times 1.7 \times 1.7 = 4.913 \]
- Next, we calculate \((1.2)^3\):
\[ (1.2)^3 = 1.2 \times 1.2 \times 1.2 = 1.728 \]

### Step 2: Subtract the two cubes
Now, we subtract the two results:
\[ (1.7)^3 - (1.2)^3 = 4.913 - 1.728 = 3.185 \]

### Step 3: Calculate \((1.7)^2\), \((1.2)^2\), and \(1.7 \times 1.2\)
- Calculate \((1.7)^2\):
\[ (1.7)^2 = 1.7 \times 1.7 = 2.89 \]
- Calculate \((1.2)^2\):
\[ (1.2)^2 = 1.2 \times 1.2 = 1.44 \]
- Calculate \(1.7 \times 1.2\):
\[ 1.7 \times 1.2 = 2.04 \]

### Step 4: Add the results
Now, we add these three results together:
\[ (1.7)^2 + (1.7 \times 1.2) + (1.2)^2 = 2.89 + 2.04 + 1.44 = 6.37 \]

### Step 5: Divide the results
Finally, we divide the result from Step 2 by the result from Step 4:
\[ \frac{3.185}{6.37} \approx 0.5 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{0.5} \]