`((0.87) ^(3) + (0.13) ^(3))/(( 0. 87) ^(2) + (0.13) ^(2) - (0.87) xx (0.13)) ` is equal to

Options

A. `1/2`
B. `2`
C. 1
D. `2 (1)/(2)`

Answer

To solve the expression \(\frac{(0.87)^3 + (0.13)^3}{(0.87)^2 + (0.13)^2 - (0.87) \times (0.13)}\), we can follow these steps:

### Step 1: Calculate the numerator
The numerator is \((0.87)^3 + (0.13)^3\).

Calculating each term:
- \((0.87)^3 = 0.658503\)
- \((0.13)^3 = 0.002197\)

Now, add these two results:
\[ 0.658503 + 0.002197 = 0.660700 \]

### Step 2: Calculate the denominator
The denominator is \((0.87)^2 + (0.13)^2 - (0.87) \times (0.13)\).

Calculating each term:
- \((0.87)^2 = 0.7569\)
- \((0.13)^2 = 0.0169\)
- \((0.87) \times (0.13) = 0.1131\)

Now, combine these results:
\[ 0.7569 + 0.0169 - 0.1131 = 0.6607 \]

### Step 3: Divide the numerator by the denominator
Now we can substitute the values we calculated into the expression:
\[ \frac{0.660700}{0.6607} \]

This simplifies to:
\[ 1 \]

### Final Answer
The value of the expression \(\frac{(0.87)^3 + (0.13)^3}{(0.87)^2 + (0.13)^2 - (0.87) \times (0.13)}\) is \(1\).

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