# Question for math lovers-2

Algebra Level 3

Given x,y $$x,y\in R,\quad { x }^{ 2 }+{ y }^{ 2 }>0$$. If the maximum and minimum value of the expression $E=\frac { { x }^{ 2 }+{ y }^{ 2 } }{ { x }^{ 2 }+xy+4y^2 }$ are M and m, compute $$\frac{ 2007}{2} \times (M + m )$$.

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