Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
a,b,c are ub A.P. the prove that
(i)a^2(b+c), b^2(c+a), c^2(a+b) are in A.P.
(ii) (ab+ac)/bc, (bc+ba)/ca, (ca+bc)/ab are in A.P.
1) 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
2) (ab+ac)/bc , (bc+ba)/ac ,(ca+bc)/ab are in AP so
2(bc+ba)/ac = (ab+ac)/bc + (ac+bc)/ab we have to prove this
multiplying the equation by abc
now we get
2b2(a+c) = a2(b+c) + c2(a+b) we have to prove this
this expression is same as of eq 1 of previous ans ,so now take RHS and prove as i have done in previous ans...
Two results to remember:
If k is a constant and a,b,c are in AP, the following are also in AP-
1) ka,kb,kc
2) a+k, b+k, c+k
Using this,
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !