If `xy = 48 and x ^(2) + y ^(2) =100,` then (x +y) is

Options

A. 12
B. 16
C. 178
D. 14

Answer

To solve the problem, we need to find the value of \( x + y \) given that \( xy = 48 \) and \( x^2 + y^2 = 100 \).

### Step-by-Step Solution:

1. **Use the identity for \( (x + y)^2 \)**:
We know that:
\[ (x + y)^2 = x^2 + y^2 + 2xy \]

2. **Substitute the known values**:
We have \( x^2 + y^2 = 100 \) and \( xy = 48 \). Substitute these values into the identity:
\[ (x + y)^2 = 100 + 2(48) \]

3. **Calculate \( 2xy \)**:
Calculate \( 2xy \):
\[ 2xy = 2 \times 48 = 96 \]

4. **Combine the values**:
Now substitute back into the equation:
\[ (x + y)^2 = 100 + 96 = 196 \]

5. **Take the square root**:
To find \( x + y \), take the square root of both sides:
\[ x + y = \sqrt{196} \]

6. **Calculate the square root**:
The square root of 196 is:
\[ x + y = 14 \]

### Final Answer:
Thus, the value of \( x + y \) is \( 14 \).