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Hi @luisxxi, thanks for taking your time to help me on this question. But as I've mentioned in my post, I need help on the 3rd part. I was able to manage the first two parts myself.

Any help on this is highly appreciates.

Many thanks!

In the first part you must transform the equation so that it fits you:

((a+b+c)/a)+((a+b+c)/b)+((a+b+c)/c)>=9

1+(b/a)+(c/a)+(a/b)+1+(c/b)+(a/c)+(b/c)+1>=9

rearranging

(a/b+b/a) + (a/c+c/a) + (b/c+c/b) + 3 >=9

and you must develop the following remarkable product: 

(a-b)^2=a^2-2ab+b^2 if a=b then a^2-2ab+b^2=0

=> a^2+b^2=2ab => (a^2+b^2)/ab=2 => a/b+b/a=2

the important thing here is that you make the assumption a = b and

a=c and b=c

With that assumption you have the problem done


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