Square Trouble

Algebra Level 4

\[ \begin{eqnarray} x^{4}+ \ ax^{3}+ \ bx^{2}+ \ cx+1\\ x^{4}+2ax^{3}+2bx^{2}+2cx+1\\ \end{eqnarray} \]

Both the expressions above are perfect squares for some \(a,b,c>0\)

Find \(a+b+c\)

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