Question

if 2x +3y=12 and xy=6 find the value of 8x³+27y³​

Answer 1

(2x+3y)³ = (12)³ cubing both sides

8x³+27y³+3.2x.3y(2x+3y) =1728

8x³+27y³+ 18xy(12) = 1728

8x³+27y³+ 18(6)(12) = 1728

8x³+27y³ = 1728-1296

8x³+27y³ = 432. Ans.

hope it will help you!!!

Answer 2

The value of 8x³+27y³ is 432.

Given:

• 2x+3y=12 and xy=6

To find:

• Find the value of 8x³+27y³.

Solution:

Identity to be used:

$\boxed{\bf ( {a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) }$

Step 1:

Take equation

$2x + 3y = 12$

take cube both sides

$( {2x + 3y)}^{3} = ( {12)}^{3}$

or

open using Identity

$( {2x)}^{3} + ( {3y)}^{3} + 3(2x)(3y)(2x + 3y) = 1728$

or

$8x^{3} + 27y^{3} + 18xy(2x + 3y) = 1728$

Step 2:

Place the value of xy and 2x+3y

$8x^{3} + 27y^{3} + 18(6)(12) = 1728$

or

$8x^{3} + 27y^{3} + 1296= 1728$

or

$8x^{3} + 27y^{3} = 1728 - 1296$

or

$8x^{3} + 27y^{3} = 432$

Thus,

Value of 8x³+27y³ is 432.

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