Question

find the value of 27x^3+8y^3 if 3x+2y=14 and xy=18

Answer 1

${(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(xy)$
apply cubing on both sides to the equation 3x+2y=14 and given quantity is xy=18. =>
${(3x + 2y)}^{3} = {(3x)}^{3} + {(2y)}^{3} +$
$3(3x)(2y)(3x + 2y)$
=>
${(14)}^{3} = 27 {x}^{3} + 8 {y}^{3} + 18xy(3x + 2y)$
=>
$2744 = 27{x}^{3} + 8 {y}^{3} + 18(18)(14)$
=>
$2744 - 4536 = 27 {x}^{3} + 8 {y}^{3}$
=>
$27 {x}^{3} + {8 y}^{3} = \: - 1792$
therefore -1792 is the answer. Hope it helps you...
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