CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If a,bandc be distinct, +veandinH.P., then an+cnis


A

>bn

No worries! Weβ€˜ve got your back. Try BYJUβ€˜S free classes today!
B

>2bn

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

<bn

No worries! Weβ€˜ve got your back. Try BYJUβ€˜S free classes today!
D

<2bn

No worries! Weβ€˜ve got your back. Try BYJUβ€˜S free classes today!
Open in App
Solution

The correct option is B

>2bn


Explanation for the correct option:

Step 1: Apply the A.M and G.M inequality to an andcn

We have given a,b,care distinct, positive, and in H.P.

let's consider two numbersan andcn.

and we know thatA.M.>G.M.>H.M. for distinct numbers.

⇒A.M>G.M⇒an+cn2>ancn⇒an+cn>2(ancn)12⇒an+cn>2(ac)n2........(1)

Step 2: Apply the G.M and H.M inequality to a andc

a,b,c are in H.P.

b is the H.M ofa andc.

G.M>H.M⇒ac>b⇒(ac)n>bn⇒(ac)n2>bn takingnth power on both sides.

β‡’2(ac)n2>2bn.........(2) Multiplying both the sides with'2'

From(1) and(2),

an+cn>2bn

Hence, the correct option is(B).


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Arithmetic Progression
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon