New Year Countdown - 9

Algebra Level 4

Consider an inequality \( (a + b)^{2} - (ab + bc + ca + 1) + 2 > 0\) where a,b,c are real. Now for the above inequality the corresponding range of values of \(c^{2}\) can be expressed in the form of \(c^{2}<N\) where N is an Integer. Then find N mod 3.

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