Question

27acube+64bcube if 3a+4b is equal to 10 and ab equal to 2 find answer

Answer 1

Here Given that

( 3a + 4b ) = 10

Cubing both sides

( 3a + 4b )³ = 10³

(3a)³ + (4b)³ +3(3a)(4b)(3a + 4b) = 1000 [∵ (a + b)³ = a³ + b³ + 3ab(a + b)]

27a³ + 64b³ +36ab(3a + 4b) = 1000

27a³ + 64b³ + 36×2×10 = 1000 [Putting ab = 2 and (3a + 4b) = 10]

27a³ + 64b³ = 1000 - 720

27a³ + 64b³ = 280