Question

if 3x +2y =a and xy =b find 27x^3+64y^3​

Answer 1

Answer:

81

Step-by-step explanation:

Correct question -----> I think correct question is ,

3x + 4y = 9 and xy = 2 , find value of

( 27x³ + 64 y³ )

Given---> 3x + 4y = 9 , xy = 2

To find-----> We know that,

( a + b )³ = a³ + b³ + 3ab ( a + b )

Putting a = 3x , b = 4y , we get,

( 3x + 4y )³ = ( 3x )³ + ( 4y )³ + 3 (3x) ( 4y ) ( 3x + 4y )

Putting , 3x + 4y = 9 , in it we get,

( 9 )³ = 27x³ + 64 y³ + 36 xy ( 9 )

Putting xy = 2 , in it , we get,

=> 729 = 27x³ + 64y³ + 36 × 2 × 9

=> 729 - 648 = 27x³ + 64y³

=> 27x³ + 64y⁴ = 81

Additional identity ----->

1) ( a - b )³ = a³ - b³ - 3ab ( a - b )

2) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

3) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )