An algebra problem by Sal Gard

Algebra Level 4

If the largest real root of \(x^6-4x^4-2x^3+4x^2+4x+1=0\) can be expressed as \(\dfrac{\sqrt a+b}{c}\), with \(a\) square-free and \(b\) and \(c\) are relatively prime, find \({(abc)}^2+1\)

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