If 3a + 2b = 27 and 27a3 + 8b3 = 1458, then find 2ab.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 75.
(x + y)3 = x3 + y3 + 3xy(x + y)
(3a + 2b)3 = (3a)3 + (2b)3 + 3 × 3a × 2b(3a + 2b)
⇒ (27)3 = 27a3 + 8b3 + 18ab(27)
⇒ 19683 = 1458 + 486ab
⇒ 486ab = 19683 - 1458 = 18225
⇒ 243(2ab) = 18225
⇒ 2ab = 18225/243 = 75