# Cool inequality

Algebra Level 5

Let $$x, y, z$$ be positive real numbers such that: $$x^2+y^2+z^2+1=2(xy+yz+zx)$$.

The minimum value of $$P=3x+2y+6z$$ is $$\alpha$$ iff $$x=\beta; y=\gamma; z=\delta$$.

And $$\alpha+\beta+\gamma+\delta=\dfrac{m}{n}$$ where $$m$$ and $$n$$ are co-prime positive integers.

What is the value of $$m+n$$?

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