Quartic with no rational solutions

Algebra Level 5

x42x28x3=0 x^4 - 2x^2 - 8x - 3 = 0

Let a,b,ca,b,c and dd denote the roots of the equation above. And suppose we denote 2n+2m=a+b+c+d2\sqrt n + 2\sqrt m = |a| + |b| + |c| + |d| for positive integers mm and nn, find the value of m2+n2m^2 + n^2 .

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