Question

If 2x+3y= 13 and xy= 6 find the value of 8x cube + 27y cube

Answer 1

Answer:

$( {2x + 3y})^{3} = ( {2x})^{3} + ( {3y})^{3} + 3 \times 2x \times 3y(2x + 3y) \\ ( {13})^{3} = 8 {x}^{3} + 27 {y}^{3} + 18xy \times 13 \\ 2197 = 8 {x}^{3} + 27 {y}^{3} + 18 \times 6\times 13\\ 2197 = 8 {x}^{3} + 27 {y}^{3} + 1404 \\ 2197 - 1404 = 8 {x}^{3} + 27 {y}^{3} \\ 793 = 8 {x}^{3} + 27 {y}^{3} \\ \implies \: 8 {x}^{3} + 27 {y}^{3} = 793$

Answer 2

Step-by-step explanation:

Given :

2x + 3y = 13 and xy = 6

To find :

value of 8x³ + 27y³

 

Solution :  

By using the identity, (a + b)³ = a³ + b³ + 3ab(a + b)  

On cubing 2x + 3y = 13 both sides,  

(2x + 3y)³ = (13)³

(2x)³ + (3y)³ + 3( 2x )(3y) (2x + 3y) = 2197

8x³ + 27y³ + 18xy(2x + 3y) = 2197

8x³ + 27y³ + 18 x 6 x 13 = 2197

8x³ + 27y³ + 1404 = 2197

8x³ + 27y³ = 2197 – 1404  

8x³ + 27y³ = 793

Hence the value of  8x³ + 27y³ is  793.

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