If `a = 2. 34 , b = 3. 121 and c =- 5. 461, ` then the value of `a ^(3) + b ^(3) + c ^(3) - 3 abc ` is:

Options

A. `-1`
B. `0`
C. 1
D. 2

Answer

To solve the problem, we need to find the value of \( a^3 + b^3 + c^3 - 3abc \) given \( a = 2.34 \), \( b = 3.121 \), and \( c = -5.461 \).

### Step-by-Step Solution:

1. **Calculate \( a + b + c \)**:
\[ a + b + c = 2.34 + 3.121 - 5.461 \]
- First, add \( a \) and \( b \):
\[ 2.34 + 3.121 = 5.461 \]
- Now, subtract \( c \):
\[ 5.461 - 5.461 = 0 \]

**Hint**: Check if the sum of the numbers equals zero.

2. **Use the identity for cubes**:
Since \( a + b + c = 0 \), we can use the identity:
\[ a^3 + b^3 + c^3 = 3abc \]
This means:
\[ a^3 + b^3 + c^3 - 3abc = 0 \]

**Hint**: Recall the identity that relates the sum of cubes to the product of the numbers when their sum is zero.

3. **Final Calculation**:
From the identity, we have:
\[ a^3 + b^3 + c^3 - 3abc = 0 \]

Thus, the value of \( a^3 + b^3 + c^3 - 3abc \) is \( 0 \).

### Conclusion:
The answer is \( 0 \).