Square Trouble

Algebra Level 4

x4+ ax3+ bx2+ cx+1x4+2ax3+2bx2+2cx+1 \begin{aligned} x^{4}+ \ ax^{3}+ \ bx^{2}+ \ cx+1\\ x^{4}+2ax^{3}+2bx^{2}+2cx+1\\ \end{aligned}

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

Find a+b+ca+b+c

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