Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
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
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
if a, b, c are three distinct positive reals in hp and n doesn`t lie between 0 and 1 then prove a^n+c^n>2b^n if a, b, c are three distinct positive reals in hp and n doesn`t lie between 0 and 1 then prove a^n+c^n>2b^n
Please find the answer to your question belowWe know that AM>GMAs a,b,c are in HP(an+cn)/2>\sqrt{a^{n}c^{n}}…............(1)But GM>HMso\sqrt{ac}>bor\sqrt{a^{n}c^{n}}>bn..................(2)So from 1 and 2(an+cn)/2>\sqrt{a^{n}c^{n}}>bnan+cn>2bn
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -