If `x=1, y=2 and z=3` then `(x^(2)+y^(2)+z^(2))=?`

Options

A. 6
B. 12
C. 14
D. 15

Answer

To solve the problem, we need to calculate the expression \( x^2 + y^2 + z^2 \) using the given values \( x = 1 \), \( y = 2 \), and \( z = 3 \).

### Step-by-Step Solution:

1. **Identify the values**: We know that \( x = 1 \), \( y = 2 \), and \( z = 3 \).

2. **Write the expression**: We need to evaluate \( x^2 + y^2 + z^2 \).

3. **Substitute the values into the expression**:
\[ x^2 + y^2 + z^2 = (1)^2 + (2)^2 + (3)^2 \]

4. **Calculate each square**:
- \( (1)^2 = 1 \)
- \( (2)^2 = 4 \)
- \( (3)^2 = 9 \)

5. **Add the squared values together**:
\[ 1 + 4 + 9 \]

6. **Perform the addition**:
- First, add \( 1 + 4 = 5 \)
- Then, add \( 5 + 9 = 14 \)

7. **Final result**: Therefore, \( x^2 + y^2 + z^2 = 14 \).

### Final Answer:
\[ x^2 + y^2 + z^2 = 14 \]