JEE Advanced: Quadratic equations & inequations

Algebra Level 4

If set of all possible values of \(k\) for which every solution of the inequality \({ x }^{ 2 }-(3k-1)x+2k^{ 2 }-3k-2\ge 0\) is also a solution of the inequality \({ x }^{ 2 }-1\ge 0\) are \([l,m]\), then find the value of \(l+m\).

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