# Have you tried multivariable polynomials?

Algebra Level 5

$\begin{eqnarray} P(x+y, x-y)&=&2 P(x,y) \\ P(1,1)&=&4 \\ P(2,3)&=&23 \end{eqnarray}$There is just one non-zero polynomial $$P(x,y)$$ with real coefficients that satisfies the properties given above.

What will be the value of $$P\left (\dfrac{8}{\sqrt{7}},-\dfrac{4}{\sqrt{7}} \right)$$?

###### This problem is from second stage of Iranian mathematical olympiads 2007 and belongs to this set.
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