Solveeit Logo
Login

Question

Question: If \(a , b , c\) are in A.P., then \(( a + 2 b - c )\) \(( 2 b + c - a )\) \(( c + a - b )\) equ...

If a,b,ca , b , c are in A.P., then (a+2b−c)( a + 2 b - c ) (2b+c−a)( 2 b + c - a ) (c+a−b)( c + a - b ) equals.

A

12abc\frac { 1 } { 2 } a b c

B

abc

C

2 abc

D

4 abc

Answer

4 abc

Explanation

Solution

(a+2b−c)(2b+c−a)(c+a−b)( a + 2 b - c ) ( 2 b + c - a ) ( c + a - b )

=(a+a+c−c)(a+c+c−a)(2b−b)= ( a + a + c - c ) ( a + c + c - a ) ( 2 b - b ) =4abc= 4 a b c

(∵a,b,c( \because a , b , c are in A.P., ∴2b=a+c\therefore 2 b = a + c ) .