Question

if 3x+2y=14and xy=8 find 27x3 +8y3

Answer 1

(3x + 2y) = 14


Cube on both sides,


(3x + 2y)³ = 14³

(3x)³ + (2y)³ + 3(3x + 2y)(3x × 2y) = 2744

27x³ + 8y³ + 3(14)(6xy) = 2744

27x³ + 8y³ + 3(14)(6)(8) = 2744

27x³ + 8y³ + 2016 = 2744

27x³ + 8y³ = 2744 - 2016

27x³ + 8y³ = 728





$.$


I hope this will help you



(-:

Answer 2

Hello friends!!

Here is your answer :

$3x + 2y = 14 \: \: \: \: \:$

Cube on both sides,


${(3x + 2y)}^{3} = {(14)}^{3}$


Using identity :

( a + b )³ = a³ + b³ + 3ab ( a + b )


$= > {(3x)}^{3} + {(2y)}^{3} + 3 \times 3x \times 2y(3x + 2y) = 14 \times 14 \times 14$


Putting the value of 3x + 2y = 14

$= > 27 {x}^{3} + {8y}^{3} + 18xy(14) = 196 \times 14$


Putting the value of xy = 8


$= > 27 {x}^{3} + 8 {y}^{3} + 18(8)(14) = 2744$

$= > 27 {x}^{3} + 8 {y}^{3} + 2016 = 2744$


$= > 27 {x}^{3} + 8 {y}^{3} = 2744 - 2016$



$= > 27 {x}^{3} + 8 {y}^{3} = 728$



Hope it helps you.. ^_^

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