Question

a/b+b/a=3 then (a³/b³)+(b³+a³)=?​

Answer 1

Answer:

- 54

Step-by-step explanation:

a/b + b/a = 3

cubing both the sides

( a/b + b/a )^3 = 3^3

( a/b)^3 + (b/a) ^3 + 3[(a/b)(b/a)](a/b + b/a) = 27

(a³/b³) + (b³+a³) + 3 ( ab/ab) ( a/b + b/a ) = 27

(a³/b³) + (b³+a³) + 3 ( 1 ) ( a/b + b/a ) = 27

(a³/b³) + (b³+a³) + 3 ( a/b + b/a ) = 27

(a³/b³) + (b³+a³) + 3 ( 27 ) = 27

(a³/b³) + (b³+a³) + 81 = 27

(a³/b³) + (b³+a³) = 21 - 81

(a³/b³) + (b³+a³) = - 54

Note :

(a + b)³ = a³ + b³ + 3ab(a+b)