Weird Polynomial Relation

Algebra Level 2

Let P(x)P(x) a polynomial in xx with real coefficients such that for all real numbers x,y,zx, y, z satisfying xy+yz+zx=1,xy+yz+zx=1, P(x)+P(y)+P(z)=P(x+y+z).P(x)+P(y)+P(z)=P(x+y+z). Furthermore, P(0)=1P(0)=1 and P(1)=4.P(1)=4. What is the value of P(2017)?\sqrt{P(2017)}?

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