Math Help - proove number inequality

1. proove number inequality

$a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.$

Then prove that

$\left( a+\dfrac{1}{b}\right).\left(b+\dfrac{1}{c}\right). \left(c+\dfrac{1}{a}\right)\geq \left(\dfrac{10}{3}\right)^3$

Anyone an idea on how to start with this exercise?

2. Re: proove number inequality

Originally Posted by wnvl
$a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1.$

Then prove that

$\left( a+\dfrac{1}{b}\right).\left(b+\dfrac{1}{c}\right). \left(c+\dfrac{1}{a}\right)\geq \left(\dfrac{10}{3}\right)^3$

Anyone an idea on how to start with this exercise?
What's the point of defining $d$ if it doesn't appear in the inequality?

3. Re: proove number inequality

Originally Posted by alexmahone
What's the point of defining $d$ if it doesn't appear in the inequality?
$a,b,c,d\in\mathbb{R^{+}}\;\;,a+b+c+d=1$

This is a way of stating that 0<a+b+c<1