0

Guest

Courses New

if a,b,c are in ap then a^2(b+c)+b^2(a+c)+c^2(a+b)=----------

if a,b,c are in ap then a^2(b+c)+b^2(a+c)+c^2(a+b)=----------

Grade:11

3 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
http://www.askiitians.com/forums/Algebra/22/23308/sequences-and-series.htm
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

if a2(b+c) , b2(a+c), c2(a+b) are in AP then

2b2(a+c) = a2(b+c) + c2(a+b) (we have to prove this) ..............................1
RHS:
= a2 (b+c) + c2 (a+b)
= a2b +a2c +c2a +c2b
=b(a2 +c2) + ac(a+c)
since a,b,c are in AP so b=a+c/2
RHS = (a+c)(a2 +b2)/2 + ac(a+c)
=(a+c)(a2 +b2 +2ac)/2
=(a+c)3 /2 or 2(a+c) b2 (after putting a+c =b)
hence proved

Thanks and Regards
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

if a2(b+c) , b2(a+c), c2(a+b) are in AP then

2b2(a+c) = a2(b+c) + c2(a+b) (we have to prove this) ..............................1
RHS:
= a2 (b+c) + c2 (a+b)
= a2b +a2c +c2a +c2b
=b(a2 +c2) + ac(a+c)
since a,b,c are in AP so b=a+c/2
RHS = (a+c)(a2 +b2)/2 + ac(a+c)
=(a+c)(a2 +b2 +2ac)/2
=(a+c)3 /2 or 2(a+c) b2 (after putting a+c =b)
hence proved

Thanks and Regards

Think You Can Provide A Better Answer ?

Other Related Questions on 9 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More