Question

If 3x+2y=12 and xy=6, then find the value of 27x^3+8y^3

Answer 1

Given :

• 3x + 2y = 12
• xy = 6

To find :

• 27x³ + 8y³

Solution :

• Using identity (a + b)³ = a³ + b³ + 3ab ( a + b)

(3x + 2y)³

12³ = (3x)³ + (2y)³ + 3 × 3x × 2y ( 3x + 2y)

1728 = 27x³ + 8y³ + 3 × 3 × 2 xy ( 12)

1728 = 27x³ + 8y³ + 18 × 6 (12)

1728 = 27 x³ + 8 y³ + 1296

1728 - 1296 = 27x³ + 8y³

432 = 27x³ + 8y³

Or

27 x³ + 8y³ = 432

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1. (a + b)² = a² + b² + 2ab
2. ( a - b)² = a² + b² - 2ab
3. ( a+ b)(a - b) = a² - b²
4. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
5. ( a + b)³ = a³ + b³ + 3ab (a + b)
6. ( a - b)³ = a³ - b³ - 3ab ( a - b)
7. a³ + b³ + c³ - 3xyz = ( a + b + c) ( a² + b² + c² - ab - bc - ca)
8. a³ + b³ = ( a + b) ( a² + b² - ab)
9. a³ - b³ = ( a - b) (a² + b² + ab)