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

Answer

To solve the problem, we need to find the value of \( a - b \) given the equations \( a^2 + b^2 = 73 \) and \( ab = 24 \). We can use the identity:

\[ (a - b)^2 = a^2 + b^2 - 2ab \]

### Step-by-step Solution:

1. **Write down the identity**:
\[ (a - b)^2 = a^2 + b^2 - 2ab \]

2. **Substitute the known values**:
We know \( a^2 + b^2 = 73 \) and \( ab = 24 \). Substitute these values into the identity:
\[ (a - b)^2 = 73 - 2 \cdot 24 \]

3. **Calculate \( 2ab \)**:
Calculate \( 2ab \):
\[ 2 \cdot 24 = 48 \]

4. **Substitute back into the equation**:
Now substitute \( 48 \) back into the equation:
\[ (a - b)^2 = 73 - 48 \]

5. **Perform the subtraction**:
Calculate \( 73 - 48 \):
\[ (a - b)^2 = 25 \]

6. **Take the square root**:
To find \( a - b \), take the square root of both sides:
\[ a - b = \sqrt{25} \]

7. **Calculate the final result**:
Since \( \sqrt{25} = 5 \):
\[ a - b = 5 \]

### Final Answer:
Thus, the value of \( a - b \) is \( 5 \).

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