Question

If 2x +3y = 13 and xy = 6, find the value of 8x3 + 27y3

Answer 1

Step-by-step explanation:

$(2x + 3y) {}^{3} = ( {13})^{3}$

$8 {x}^{3} + 27 {y}^{3} + 3(2x)(3y)(2x + 3y)$

$8 {x}^{3} + 27 {y}^{3} + 18(6)(2x + 3y) = 2197$

$8 {x}^{3} + 27 {y}^{3} + 18(6)(13) = 2197$

$8x {}^{3} + 27 {y}^{3} = 2197 - 18 \times 6 \times 13$

$8 {x}^{3} + 27 {y}^{3} = 793$

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