Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Management
  • If , then the minimum value of <img alt="\frac{ab}{c^{2}}+\frac{bc}{a^{2}}+\frac{ca}{b^{2}}" src="https:/

If a,b,c>0, then the minimum value of \frac{ab}{c^{2}}+\frac{bc}{a^{2}}+\frac{ca}{b^{2}} is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

Let \;a_{1}=\frac{a b}{c^{2}}, a_{2}=\frac{b c}{a^{2}}, a_{3}=\frac{c a}{b^{2}}

and apply AM\geqslant GM relation

\begin{aligned} & \frac{a_{1}+a_{2}+a_{3}}{3} \geqslant\left(a_{1} \cdot a_{2} \cdot a_{3}\right)^{1 / 3} \\ \Rightarrow & \frac{a b}{c^{2}}+\frac{b c}{a^{2}}+\frac{c a}{b^{2}} \geqslant 3\left(\frac{a b}{c^{2}} \cdot \frac{b c}{a^{2}} \cdot \frac{c a}{b^{2}}\right)^{1 / 3} \\ \Rightarrow & \frac{a b}{c^{2}}+\frac{b c}{a^{2}}+\frac{c a}{b^{2}} \geqslant 3 \end{aligned}

So minium value is 3.

Posted by

vinayak

View full answer

Similar Questions

Trending Articles/News

anam-khan

CAT 2024: IIM Kozhikode revises admission criteria; 10% drop in Class 10 weightage
anam-khan

CAT 2024 preparation strategy for last 10 days; section-wise tips, best books
anam-khan

CAT official mock test link 2024 out; IIM Calcutta issues navigation guide at iimcat.ac.in

Latest Question