Question

If 3x-2y=13 and xy=5,find the value of 27x3-8y3

Answer 1

Answer:

3367

Step-by-step explanation:

Given that,

3x - 2y = 13

xy = 5

To find the value of 27x^3 - 8y^3.

Further solving, we get,

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

But, we know that,

• ${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

Therefore, we will get,

$= (3x - 2y)( {(3x)}^{2} + (3x)(2y) + {(2y)}^{2} ) \\ \\ = (3x - 2y)( {(3x - 2y)}^{2} + 2(3x)(2y) + (3x)(2y)) \\ \\ = ( 3x - 2y)( {(3x - 2y)}^{2} + 3(3x)(2y)) \\ \\ = (3x - 2y)( {(3x - 2y)}^{2} + 18xy)$

Substituting the values, we get,

$= 13( {(13)}^{2} + 18(5)) \\ \\ = 13(169 + 90) \\ \\ = 13 \times 259 \\ \\ = 3367$

Hence, required answer is 3367.

Answer 2

Answer:

4667

Step-by-step explanation:

3

x

−

2

y

=

13

⟹

(

3

x

−

2

y

)

2

=

13

2

⟹

9

x

2

+

4

y

2

−

12

x

y

=

169

⟹

9

x

2

+

4

y

2

+

6

x

y

=

169

+

18

x

y

=

169

+

90

=

359

27

x

3

−

8

y

3

=

(

3

x

)

3

−

(

2

y

)

3

=

(

3

x

−

2

y

)

(

9

x

2

+

4

y

2

+

6

x

y

)

=

(

13

)

(

359

)

=

4667