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.
×

Problem Loading...

Note Loading...

Set Loading...