Question

find the value of of27xcube+8y cube,If​

Answer 1

Given that,

1. 3x + 2y = 20

2. xy = 14 / 9

We have to find,

→ 27x³ + 8y³

We must use the identity:

a³ + b³ = (a + b)(a² + b² - ab)

So, let,

a = 3x

b = 2y

→ a + b = 3x + 2y = 20

→ a³ + b³ = 27x³ + 8y³

→ ab = 6xy = 6 • 14 / 9 = 28 / 3

=> 3ab = 3 • 28 / 3 = 28

=> 3x + 2y = 20

=> a + b = 20

=> (a + b)² = 20²

=> a² + b² + 2ab = 400

=> a² + b² + 2ab - 3ab = 400 - 3ab

=> a² + b² - ab = 400 - 28

=> a² + b² - ab = 372

Now,

27x³ + 8y³

=> a³ + b³

=> (a + b)(a² + b² - ab)

=> 20 • 372

=> 7440

Hence 7440 is the answer.