Question

if 3x - 2 Y is equal to 5 and X Y is equal to 6 find the value of 27 x cube minus 8 y cube​

Answer 1

Answer:

665

Step-by-step explanation:

Given that,

3x - 2y = 5

xy = 6

To find tha value of,

$27 {x}^{3} - 8 {y}^{3}$

Therefore, we will get,

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

But, we know that,

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

Therefore, we will get,

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

Substituting the values, we get,

$= 5( {5}^{2} + 18 \times 6) \\ \\ = 5(25 + 108) \\ \\ = 5 \times 133 \\ \\ = 665$

Hence, required value is 665.

Answer 2

Answer:

665

Step-by-step explanation:

First solve x and y and then substitute the values in 27x³-8y³