Question

find(a/b)^3+(b/c)^3+(c/a)^3-3 by using suitable identity ​

Answer 1

Answer:

(a/b+b/c+c/a){a²/b²+b²/c²+c²/a²-a/c-b/a-c/b}

Step-by-step explanation:

Given,

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

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

= (a/b+b/c+c/a){(a/b)²+(b/c)²+(c/a)²-(a/b)(b/c)-(b/c)(c/a)-(a/b)(c/a)}

= (a/b+b/c+c/a){a²/b²+b²/c²+c²/a²-a/c-b/a-c/b}

Hence, the required answer =

(a/b+b/c+c/a){a²/b²+b²/c²+c²/a²-a/c-b/a-c/b}