Có: a + b = 12
⇒ a = 12 - b
Mà: a.b = -18
Thay a = 12 - b vào, ta có:
(12 - b).b = -18
⇔ 12b - b² + 18 = 0
⇔ b² - 12b - 18 = 0
⇔ \(\left[ \begin{array}{l}b=6+3√6\\b=6-3√6\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}a=12 - 6 - 3√6 = 6-3√6\\a=12 - 6+3√6 = 6+3√6\end{array} \right.\)
=> a³ + b³ = \(\left[ \begin{array}{l}(6+3√6)³ + (6-3√6)³\\(6-3√6)³+(6+3√6)³\end{array} \right.\)
= (6 + 3√6)³ + (6 - 3√6)³ = (6-3√6)³+(6+3√6)³
= 2376
Vậy a³ + b³ = 2376.
