Question

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Find the value of 27x³+8y³if 3x+2y=20 and xy=11/9

Answer 1

$27 {x}^{3} + 8 {y}^{3} = {(3x)}^{3} + {(2y)}^{3} \\ = {(3x + 2y)}^{3} - 3 \times 3x \times 2y \times (3x + 2y) \\ = {(3x + 2y)}^{3} - 18xy \times (3x + 2y) \\ = {20}^{3} - 18 \times \frac{11}{9} \times 20 \\ = 8000 - 440 = 7560$