Thinking about roots

Algebra Level 4

If \(a\), \(b\) and \(c\) are side lengths of a triangle \(ABC\) such that \[ x^2 - 2(a+b+c)x +3k(ab+bc+ca) =0\] where \(k<\dfrac {a} {b}\), has real roots, find \(a+b\).

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