Find The Maximum

Algebra Level 4

As x,y,zx,y,z range over all positive real numbers satisfying xy+yz+zx=xyz(x+y+z),xy+yz+zx= xyz(x+y+z), the maximum value of 1(2x+y+z)2+1(x+2y+z)2+1(x+y+2z)2\dfrac{1}{(2x+y+z)^2} + \dfrac{1}{(x+2y+z)^2} + \dfrac{1}{(x+y+2z)^2} can be expressed as ab,\dfrac{a}{b},where a,ba,b are coprime positive integers. Find a+b.a+b.

Details and assumptions

  • This problem is not original.
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