Given positive real numbers \( (x,y,z) \) such that \( xy + yz + xz = 5\). The minimum value of \[ \dfrac{x^2}{y^3} + \dfrac{y^2}{z^3} + \dfrac{z^2}{x^3} + x + y + z \]

is \(

\frac{ a \sqrt{b} } { c} \), where \(a, b, \) and \(c\) are positive integers, \( \gcd(a,c) = 1 \) , and \(b\) is square free. What is the value of \( a + b + c \)?

For more problem maximum and minimum value, click here

×

Problem Loading...

Note Loading...

Set Loading...