### The values of k that satisfies the inequation \[(k-12) \geq k^2 - 9k + 12\] are in the range \[[a, b]\]. Then find the values of a and b.

To solve this inequality, we first need to rearrange the terms to one side of the inequality. This gives us:

k^2 - 10k + 12 ≤ 0

This is a quadratic inequality. To solve it, we first need to find the roots of the corresponding quadratic equation, which are the values of k for which:

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