New year gift 2
Algebra
Level
5
Positive real numbers \(a\), \(b\), and \(c\) are such that \(\dfrac{1}{a}+ \dfrac{1}{b}+ \dfrac{1}{c} =a+b+c\). And if
\[\frac{1}{(2a+b+c)^2}+ \frac{1}{(a+2b+c)^2}+ \frac{1}{(a+b+2c)^2} \leq \dfrac{p}{q} \]
where \(p\) and \(q\) are coprime positive integers. Find \(p+q\).
by
Atul Shivam