Question

find the value of the following 8x³+27y³ if 2x+3y=14 and xy=8

Answer 1

Given : 2x + 3y = 14 and xy = 8

To find the value of $8x^{3} +27y^{3}$

Identity: $a^{3} +b^3} =(a+b)^{3} - 3ab(a+b)$

Now, we shall calculate $8x^{3}+27y^{3}$

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

or, $8x^{3} +27y^{3} =(2x+3y)^{3} - 18xy(2x +3y) -------(i)$

Now, substituting the given values in equation (i), we have

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

or, = 2744 - 2016

or, = 728

Hence, the required value of $8x^{3}+27y^{3}$ will be 728.

Answer 2

Answer:

Given

2x + 3y = 14 and xy = 8

8x³ + 27y³

(2x)³ + ( 3y)³

( 2x + 3y)³ – 3 × 2x × 3y ( 2x + 3y)

(2x + 3y)³ – 18xy ( 2x + 3y)

putting 2x + 3y = 14 and xy = 8

(14)³ = 18×18 (14)

2744 – 144 × 4

2744 – 2016

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