If a + b = 4 and ab = -12, find

(i) a - b

(ii) a² - b².

(i) We know that,

(a - b)² = a² + b² - 2ab

(a - b)² = a² + b² + 2ab -2ab - 2ab

(a - b)² = (a + b)² - 4ab

(a - b) = $\sqrt{(a + b)^2 - 4ab}$

Substituting values we get,

$\Rightarrow (a - b) = \sqrt{(4)^2 - 4 \times (-12)} \\[1em] \Rightarrow (a - b) = \sqrt{16 + 48} \\[1em] \Rightarrow (a - b) = \sqrt{64} \\[1em] \Rightarrow (a - b) = \pm 8.$

Hence, a - b = ±8.

(ii) We know that,

a² - b² = (a + b)(a - b).

Substituting values we get,

⇒ a² - b² = 4 × ±8 = ±32.

Hence, a² - b² = ±32.