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Real numbers $x$ and $y$ satisfy $2 x + 3 y = 12$ and $x y = 6$ . Find $8 x^{3} + 27 y^{3}$ .

Competition practiceAlgebra

A432
B1728
C1296
D216

Step-by-Step Solution

8 x^{3} + 27 y^{3} = (2 x + 3 y)^{3} - 3 \cdot (2 x) (3 y) (2 x + 3 y) = 1728 - 18 \times 6 \times 12 = 1728 - 1296 = 432. (x = 3, y = 2.)

Answer: A) 432

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