Question

if x - 2y = -11 and 3xy = 8 , find the value of x^3 - 8y^3

Answer 1

$x + 2y = 5$

$\huge\pink{cu}\green{be}\red{ing}$

$( {x + 2y)}^{3} = {5}^{3} \\ \\ \\ \\ = > {x}^{3} + {8y}^{3} + 3 x \times 2y(x + 2y) = 125 \\ \\ \\ = > {x}^{3} + {8y}^{3} + 3 x \times 2y(5) = 125 \\ \\ \\ = > {x}^{3} + {8y}^{3} + 30xy= 130$

Answer 2

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$\small\star\underline\bold\red{Given-}$

• x - 2y = -11
• 3xy = 8

$\small\star\underline\bold\red{To find-}$

• x³ - 8y³

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$\small\star\underline\bold\red{Solution-}$

(x - 2y)³ = (-11)³

$\implies$ x³ - 8y³ - 3x•2y( x -2y ) = -1331

$\implies$ x³ - 8y³ - 2(8)( -11 ) = -1331

$\implies$ x³ - 8y³ + 176 = -1331

$\implies$ x³ - 8y³ = -1331 -176

$\implies$ x³ - 8y³ = -1507

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