Question

14. If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³.​

Answer 1

Solution:

Given,

→ 3x + 2y = 9 and,

→ xy = 3

Using identity a³ + b³ = (a + b)³ - 3ab(a + b), we get,

→ (3x)³ + (2y)³ = (3x + 2y)³ - 3 × 3x × 2y(3x + 2y)

→ 27x³ + 8y³ = 9³ - 18 × 3 × 9

→ 27x³ + 8y³ = 9³ - 9² × 6

→ 27x³ + 8y³ = 9²(9 - 6)

→ 27x³ + 8y³ = 81 × 3

→ 27x³ + 8y³ = 243

★ So, the value of 27x³ + 8y³ is 243.

Answer:

• 27x³ + 8y³ = 243

Additional Identities:

• (a - b)² = a² - 2ab + b²
• (a + b)² = a² + 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)

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