If 3x-2y =11 and xy=12 find 27xcube -8ycube
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7...... is right answer..
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3x - 2y = 11
take cube both sides ,
(3x -2y)³ = 11³
(3x)³ - 3(3x)²(2y) + 3(3x)(2y)² - (2y)³ = 1331
27x³ - 3(3x)(2y)(3x - 2y) - 8y³ = 1331
27x³ - 8y³ - 18xy(3x - 2y) = 1331
27x³ - 8y³ - 18 × 12 × 11 = 1331
27x³ - 8y³ = 1331 + 18 × 12 × 11
27x³ - 8y³ = 11(121 + 216) = 11 × 337
27x³ - 8y³ = 3707
take cube both sides ,
(3x -2y)³ = 11³
(3x)³ - 3(3x)²(2y) + 3(3x)(2y)² - (2y)³ = 1331
27x³ - 3(3x)(2y)(3x - 2y) - 8y³ = 1331
27x³ - 8y³ - 18xy(3x - 2y) = 1331
27x³ - 8y³ - 18 × 12 × 11 = 1331
27x³ - 8y³ = 1331 + 18 × 12 × 11
27x³ - 8y³ = 11(121 + 216) = 11 × 337
27x³ - 8y³ = 3707
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