One of the shortlisted problem of I.M.O

Algebra Level 3

Let a, b and c be positive real numbers such that a b c = 1 abc = 1 than find the maximum value of a b a 5 + b 5 + a b + b c b 5 + c 5 + b c + c a c 5 + a 5 + c a \frac{ab}{a^5+b^5+ab}+\frac{bc}{b^5+c^5+bc}+\frac{ca}{c^5+a^5+ca}


The answer is 1.

Atul Shivam by Atul Shivam , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

汶良 林
Oct 28, 2015

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Aakash Khandelwal
Oct 27, 2015

Since fraction is maximum when denominator is least. Apply AM>=GM in denominators of all three fractions

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...