The values of k that satisfies the inequation (k-12) ≥ k2-9k + 12 are in the range [a, b]. Then find the values of a and b, a=1,b=7a=0,b=7a=0;b=8a=1,b=8

To solve the inequality (k-12) ≥ k^2 - 9k + 12, we first need to rearrange the terms to one side of the inequality. This gives us:

k^2 - 10k + 24 ≤ 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 k^2 - 10k + 24 = 0. This can be done by using the quadratic formula:

k = [10 ± sqrt((10)^2 - 4124)] / (2*1) k = [10 ± sqrt(100 - 96)] / 2 k = [10 ± sqrt(4)] / 2 k = [10 ± 2] / 2 k = 5 ± 1

So the roots of the equation are k = 4 and k = 6. These are the points where the inequality changes sign.

Since the coefficient of k^2 in the inequality is positive, the inequality is satisfied for values of k between the roots. Therefore, the solution to the inequality is 4 ≤ k ≤ 6.

So, the values of a and b that satisfy the given range are a = 4 and b = 6. None of the given options match this result.