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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