# Quartic with no rational solutions

Algebra Level 5

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

Let $$a,b,c$$ and $$d$$ denote the roots of the equation above. And suppose we denote $$2\sqrt n + 2\sqrt m = |a| + |b| + |c| + |d|$$ for positive integers $$m$$ and $$n$$, find the value of $$m^2 + n^2$$.

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