`(0.86 xx 0. 86 xx 0. 86 + 0. 14 xx0.14 xx 0. 14)/(0.86 xx 0.86 - 0. 86 + 0.14 + 0.14 xx 0. 14) ` is equal to

Options

A. 1
B. 0
C. 2
D. 10

Answer

To solve the expression \((0.86 \times 0.86 \times 0.86 + 0.14 \times 0.14 \times 0.14)/(0.86 \times 0.86 - 0.86 + 0.14 + 0.14 \times 0.14)\), we can follow these steps:

### Step 1: Define Variables
Let \( a = 0.86 \) and \( b = 0.14 \). This simplifies our expression.

### Step 2: Rewrite the Expression
The expression can now be rewritten as:
\[ \frac{a^3 + b^3}{a^2 - a + b + b^2} \]

### Step 3: Apply the Sum of Cubes Formula
Recall the identity for the sum of cubes:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Using this identity, we can rewrite the numerator:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]

### Step 4: Expand the Denominator
Now, let's expand the denominator:
\[ a^2 - a + b + b^2 \]
This remains as is for now.

### Step 5: Substitute the Identity into the Expression
Substituting the identity for the numerator into our expression, we have:
\[ \frac{(a + b)(a^2 - ab + b^2)}{a^2 - a + b + b^2} \]

### Step 6: Simplify the Expression
Notice that \( a^2 - ab + b^2 \) is part of the denominator. Therefore, if \( a^2 - ab + b^2 \) is not zero, we can cancel it out:
\[ = a + b \]

### Step 7: Calculate \( a + b \)
Now, substituting back the values of \( a \) and \( b \):
\[ a + b = 0.86 + 0.14 = 1 \]

### Final Answer
Thus, the value of the original expression is:
\[ \boxed{1} \]

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