Does Trigonometric Substitution Works?
Algebra
Level
5
\[\large \dfrac { \sqrt { b^{ 2 }+2{ a }^{ 2 } } }{ ab } +\dfrac { \sqrt { { a }^{ 2 }+2c^{ 2 } } }{ ac } +\dfrac { \sqrt { { c }^{ 2 }+2{ b }^{ 2 } } }{ bc } \]
Let \(a\), \(b\) and \(c\) be positive reals satisfying \(ab+bc+ca=abc\).
If the minimum value of the expression above can be expressed as \( \sqrt m\), where \(m\) is a positive integer, find \(m\).
by
Huân Lê Quang