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Given x = y + 2 x² + y² = 34

x - y = 2 squaring, (x - y)² = 2² x² + y² - 2 x y = 4 34 - 2 x y = 4 x y = 15 =========================== 2x - 3y = 10 x y = 16

8x³ - 27 y³ = (2x - 3y) ( 4x² + 6 xy + 9 y²) = (2 x - 3y) [ (2x -3y)² + 18 xy ] = 10 * [ 10² + 18 * 16 ] ==================================== x > 0 and x² + 1/9x² = 25 / 36 (x + 1/3x)² = x² + 1/9x² + 2/3 = 25/36 + 2/3 (x + 1/3x)² = 49/36 x + 1/3x = 7/6 , we drop the negative value as x > 0.