Question

if 3x-2y=14 and xy=12 find 27x cube - 8y cube

Answer 1

hey mate
we have 3x-2y=14
and xy=12->y=12/x
substitute y in 1st equation
u will get 3x-24/x=14
3x^2-24=14x
3x^2-14x-24=0
x=14+-root(196+288)/6
=14 +-22/6
so x=6
now we will get y as 2
so now 27x^3-8y^3 =27×216-8×8=5832-64=5768
i hope u understood!!

Answer 2

Solution:

Given

3x - 2y = 14 -----( 1 )

xy = 12 ----( 2 )

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We know the algebraic identity :

a³ - b³ - 3ab( a - b ) = ( a - b )³

or

a³ - b³ = ( a - b )³ + 3ab( a - b )

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Here ,

27x³ - 8y³

= ( 3x )³ - ( 2y )³

= ( 3x - 2y )³ + 3*3x*2y ( 3x - 2y )

= 14³ + 18xy *14

= 14 ( 14² + 18 × 12 )

= 14( 196 + 216 )

= 14 × 412

= 5768

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