3x-2y=11, xy=12 find the value of 27x3-8y3
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- GIVEN THAT,
- 3x - 2y = 11 -----(1)
- xy = 12 -----(2)
- Cubing both sides in eq(1)
- We get
- (3x - 2y)³ = 11³
- (3x)³ - (2y)³ - 3(3x)(2y) (3x - 2y) = 11³
- 27x³ - 8y³ - 18xy × 11 = 11³ __ [from (1)]
- 27x³ - 8y³ - 18×12×11 = 11³ __ [from(2)]
- 27x³ - 8y³ = 11³ + 18×12×11
- = 11 (11² + 18×12)
- = 11 (121 + 216)
- = 11 × 337
- = 3707
- Hence,
- 27x³ - 8y³ = 3707
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