wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If a,b,c are in arithmetic progression, then the value of (a+2b-c)(2b+c-a)(a+2b+c)


Open in App
Solution

Finding the value of left parenthesis a space plus space 2 b space minus space c right parenthesis left parenthesis 2 b space plus space c space minus space a right parenthesis left parenthesis a space plus space 2 b space plus space c right parenthesis:

Given a,b,c are in A.P

So 2b=a+c

and (a+2b-c)(2b+c-a)(a+2b+c)....(i)

we get (a+a+c-c)(a+c+c-a)(a+a+c+c)

=(2a)(2c)(2a+2c)=8ac(a+c)=8ac(2b)=16abc

Therefore (a+2b-c)(a+2b+c)(2b+c-a)=16abc

Hence, the value of (a+2b-c)(2b+c-a)(a+2b+c) is 16abc


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Modulus
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon