Now its very strenuous

Algebra Level 4

Three positive real numbers \(a\), \(b\), and \(c\) satisfy the following equation. \[\large a+b+c=abc\] Let \[\large N = 3+\dfrac{b}{a^2}+\dfrac{c}{b^2}+\dfrac{a}{c^2}-\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)^2\] If the minimum value of \(N\) can be expressed as \(\sqrt{x}\), where \(x\) is square free positive integer. Find \(x\).

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