Question

if a, b and c are three positive real numbers then the minimum value of the expression b+c/a +c+a/b +a+b/c is

Answer 1

Do you mean:

\(b + \dfrac{c}{a} + c + \dfrac{a}{b} + a + \dfrac{b}{c} \) (which is what you wrote)

or

\(\dfrac{b + c}{a} + \dfrac{c + a}{b} + \dfrac{a + b}{c} ~~~~~ ?\)

Answer 2

@samigupta8 Please use the equation mode to input your question, otherwise it gets kinda hard to understand the question.

Answer 3

I am assuming it to be the latter one.
Simplify your expression like this :

(b/a) + (c/a) + (c/b) + (a/b) + (a/c) + (b/c)

= ( b/a + a/b) + ( c/a + a/c) + ( c/b + b/c)

Doesthis help your case ?

Answer 4

so 3 ?

Answer 5

( b/a + a/b) + ( c/a + a/c) + ( c/b + b/c)
>=1 >=1 >=1

>= 3

minimum value = 3

Answer 6

>=2 right ?
so 6 :|

Answer 7

how ?
am/gm >= 1 right ?

Answer 8

(b/a + a/b)/2 >= 1
and hence the conclusion .

Answer 9

yeah missed the /2 !

Answer 10

bt how come b/a +a/b>=1

Answer 11

kk... i understood