BdMO Online Forum

$a=p/q$
$b=q/r$
$c=r/p$
p,q,r are Positive Integer.
Find the lowest value of
#$(4+a)(4+b)(4+c)$
And
#$(1+a)(1+b)(1+c)$
Source: bigganchinta december 2016

Hint:
1. 2.

Phlembac Adib Hasan wrote: ↑

Wed Feb 14, 2018 4:59 am

Hint:
1.

$abc=1$. Now apply AM-GM.

2.

#2 directly follows from AM-GM. For #1, can you find a clever way to apply AM-GM?

THANKS ADIB VAIA.
Answer
1. 2. Is it a clever way to use $a+1/a \geq2$ to get the lowest value of# 1?