Question

(a-b) whole cube+(b-c)whole cube+(c-a) whole cube divided by (a-b)(b-c)(c-a).

Answer 1

Answer:

3

Step-by-step explanation:

Given--->

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

To find ---> Value of given expression

Solution---> We know that,

If , x + y + z = 0 , then,

x³ + y³ + z³ = 3 x y z

Let, ( a - b ) = p , ( b - c ) = q , ( c - a ) = r

p + q + r = ( a - b ) + ( b - c ) + ( c - a )

p + q + r = 0

So, p³ + q³ + r³ = 3 p q r

Putting , p = (a - b) , q = (b - c) , r = (c - a)

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

Now , returning to original problem,

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

putting (a - b)³ + (b - c )³ + (c - a)³ = 3(a-b) (b - c)

(c - a)

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

= 3

Answer 2

Step-by-step explanation:

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