First, let's expand the left side of the inequality:
(k+4)(k-4) - 6k + 5= k^2 - 4k + 4k - 16 - 6k + 5= k^2 - 6k - 11
Now let's expand the right side of the inequality:
(k-3)^2 + 4= k^2 - 6k + 9 + 4= k^2 - 6k + 13
So the inequality becomes:
k^2 - 6k - 11 > k^2 - 6k + 13
Subtracting k^2 and adding 6k on both sides, we get:
-11 > 13
This is not a true statement, so our initial assumption is incorrect. Therefore, there is no solution for this inequality.
First, let's expand the left side of the inequality:
(k+4)(k-4) - 6k + 5
= k^2 - 4k + 4k - 16 - 6k + 5
= k^2 - 6k - 11
Now let's expand the right side of the inequality:
(k-3)^2 + 4
= k^2 - 6k + 9 + 4
= k^2 - 6k + 13
So the inequality becomes:
k^2 - 6k - 11 > k^2 - 6k + 13
Subtracting k^2 and adding 6k on both sides, we get:
-11 > 13
This is not a true statement, so our initial assumption is incorrect. Therefore, there is no solution for this inequality.