Question

Find the value of a3+8b3 if a+2b=10 and ab=15

Answer 1

a + 2b = 10

ab = 15

______________[GIVEN]

a + 2b = 10

• Take cube on both sides

=> (a + 2b)³ = (10)³

=> (a)³ + 3(a)(2b) [(a + 2b)] + (2b)³ = 1000

=> a³ + 8b³ + 6ab (a + 2b) = 1000

=> a³ + 8b³ + 6(15) (10) = 1000

=> a³ + 8b³ + 900 = 1000

=> a³ + 8b³ = 1000 - 900

=> a³ + 8b³ = 100

____________________________

» Using Identity :

(a + b)³ = a³ + 3ab (a + b) + b³

OR

(a + b)³ = a³ + 3a²b + 3ab² + b³

_____________________________

a³ + 8b³ = 100

________________[ANSWER]

Answer 2

Answer:

100

Step- by-step explanation:

Given a +2b = 10 and ab = 15

Consider, a3 + 8b3 = a3 + (2b)3

                             = (a + 2b)3 − 3 × a × 2b(a + 2b)  [Since, a3 + b3 = (a + b)−             3ab(a + b)]

                             = (a + 2b)3 − 6ab(a + 2b)

                             = (10)3 − 6 × 15 × 10

                             = 1000 − 900 = 100