Explanation:

- Given the equations: \(a + b = 10\) and \(ab = 9\).

- To find \(a - b\), we use the identity: \((a - b)^2 = (a + b)^2 - 4ab\).

- Step-by-step:

- Calculate \((a + b)^2 = 10^2 = 100\).

- Substitute \(ab = 9\) into the equation: \((a - b)^2 = 100 - 4 \times 9 = 100 - 36 = 64\).

- Solve for \(a - b\): \(\sqrt{64} = 8\).

- Explanation of options:

- Option 1, 7: Incorrect, not derivable from the given conditions.

- Option 2, 5: Incorrect, doesn't satisfy derived calculations.

- Option 3, 8: Correct, matches derived values.

- Option 4, 6: Incorrect, doesn't equate from calculations.