Curious Condition

Algebra Level 5

Positive reals x,y,z33x,y,z\ge \dfrac{\sqrt{3}}{3} satisfy the condition xyz+x+yz=0xyz+x+y-z=0. If kxyzxyyzzx1kxyz-xy-yz-zx\ge 1 is always true, the the minimum value of kk can be expressed as abc\dfrac{a\sqrt{b}}{c} for positive integers a,b,ca,b,c with a,ca,c coprime and bb square-free.

What is a+b+ca+b+c?

×

Problem Loading...

Note Loading...

Set Loading...