Question

If 3x + 2y = 10 and, xy = 2.
Then Find the Value of (27x³ + 8y³)​

Answer 1

AnswEr :

• 3x + 2y = 10
• xy = 2
• (27x³ + 8y³) = ?

• we will use the cubic formula here :

⇒ 3x + 2y = 10

• Cubing Both Sides

⇒ (3x + 2y)³ = (10)³

• (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ (3x)³ + (2y)³ + 3.3x.2y(3x + 2y) = (10)³

⇒ 27x³ + 8y³ + 18xy(3x + 2y) = 1000

• Given Value of (3x + 2y) = 10 and Value of xy = 2, we will use that.

⇒ 27x³ + 8y³ + (18 × 2 × 10) = 1000

⇒ 27x³ + 8y³ + 360 = 1000

⇒ 27x³ + 8y³ = 1000 - 360

⇒ 27x³ + 8y³ = 640

∴ Hence, the Value of (27x³ + 8y³) is 640.

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• Some Important Formulae :

⋆ (a + b)² = a² + b² + 2ab

⋆ (a – b)² = a² + b² – 2ab

⋆ (a + b)³ = a³ + b³ + 3ab(a + b)

⋆ (a – b)³ = a³ – b³ – 3ab(a – b)

⋆ (a² – b²) = (a + b)(a – b)

Answer 2

Answer:

Step-by-step explanation:

Given :-

3x + 2y = 10

xy = 2

To Find :-

27x³ + 8y³) = ???

Formula to be used :-

(a + b)³ = a³ + b³ + 3ab(a + b)

Solution :-

Solving equation, we get

⇒ 3x + 2y = 10

⇒ (3x + 2y)³ = (10)³  [(a + b)³ = a³ + b³ + 3ab(a + b)]

⇒ (3x)³ + (2y)³ + 3 × 3x × 2y(3x + 2y) = (10)³

⇒ 27x³ + 8y³ + 18xy(3x + 2y) = 1000

⇒ 27x³ + 8y³ + (18 × 2 × 10) = 1000

⇒ 27x³ + 8y³ + 360 = 1000

⇒ 27x³ + 8y³ = 1000 - 360

⇒ 27x³ + 8y³ = 640

Hence, The value (27x³ + 8y³)​ is 640.