If a + 2b = 27 and $a^3 + 8b^3 = 5427$, then find the value of 2ab.
Answer & explanation
Correct answer: option 1
Given,
a + 2b = 27
a3 + 8b3 = 5427
We know that,
(A + B)3 = A3 + B3 + 3AB(A + B)
= (27)3 = 5427 + 3 × 2ab(27)
= 19683 = 5427 + 81 × 2ab
= 81 × 2ab = 14256
= 2ab = 176