If `a^2 + b^2 = 73 and ab = 24`, find : (i) `a+b`

Answer

To solve the problem, we will use the identity \( (a + b)^2 = a^2 + b^2 + 2ab \).

### Step-by-Step Solution:

1. **Write down the given equations:**
\[ a^2 + b^2 = 73 \]
\[ ab = 24 \]

2. **Use the identity for \( (a + b)^2 \):**
\[ (a + b)^2 = a^2 + b^2 + 2ab \]

3. **Substitute the known values into the identity:**
\[ (a + b)^2 = 73 + 2 \times 24 \]

4. **Calculate \( 2 \times 24 \):**
\[ 2 \times 24 = 48 \]

5. **Add the values:**
\[ (a + b)^2 = 73 + 48 = 121 \]

6. **Take the square root to find \( a + b \):**
\[ a + b = \sqrt{121} \]

7. **Calculate the square root:**
\[ a + b = 11 \]

### Final Answer:
\[ a + b = 11 \]