Verified answer

Answer: 27x³ - 8y³ = 3,707

³ - ³ = ( - )(² + + ²)

Given:

• 3x - 2y = 11

• xy = 12

To find:

• 27x³ - 8y³

27x³ - 8y³ = (3x - 2y) (9x² + 6xy + 4y²)

• 3x - 2y = 11

• (3x - 2y)² = (11)²

• 9x² - 12xy + 4y² = 121

• 9x² - 12xy + 4y² + 18xy = 121 + 18xy

• 9x² + 6xy + 4y² = 121 + 18xy

• 9x² + 6xy + 4y² = 121 + 18(12)

• 9x² + 6xy + 4y² = 121 + 216

• 9x² + 6xy + 4y² = 337

27x³ - 8y³ = (3x - 2y) (9x² + 6xy + 4y²)

27x³ - 8y³ = (11) (337)

27x³ - 8y³ = 3,707

EXPLANATION.

⇒ 3x - 2y = 11. - - - - - (1).

⇒ xy = 12. - - - - - (2).

As we know that,

Formula of :

⇒ (a - b)³ = a³ - 3a²b + 3ab² - b³.

Using this formula in this question, we get.

Cubing on both sides of the equation (1), we get.

⇒ (3x - 2y)³ = (11)³.

⇒ (3x)³ - 3(3x)²(2y) + 3(3x)(2y)² - (2y)³ = 1,331.

⇒ 27x³ - 54x²y + 36xy² - 8y³ = 1,331.

⇒ 27x³ - 8y³ - 54x²y + 36xy² = 1,331.

⇒ 27x³ - 8y³ - 18xy(3x - 2y) = 1,331.

Put the value of equation (1) and equation (2) in the equation, we get.

⇒ 27x³ - 8y³ - 18(12)(11) = 1,331.

⇒ 27x³ - 8y³ - 2,376 = 1,331.

⇒ 27x³ - 8y³ = 1,331 + 2,376.

⇒ 27x³ - 8y³ = 3,707.

∴ value of 27x³ - 8y³ is 3,707.