(з-1)^2(х-4)<0

To solve this inequality, we first need to find the critical points where the expression equals zero.

Setting the expression equal to zero:

(z-1)^2(x-4) = 0

This means that either (z-1)^2 = 0 or (x-4) = 0.

For (z-1)^2 = 0, we have z = 1. For (x-4) = 0, we have x = 4.

So, the critical points are z = 1 and x = 4.

Now, we can test the intervals created by these critical points to determine where the expression is less than zero.

1. When z < 1 and x < 4: In this case, both factors are negative, so the expression is positive.

2. When z > 1 and x < 4: In this case, the first factor is positive and the second factor is negative, so the expression is negative.

3. When z < 1 and x > 4: In this case, the first factor is negative and the second factor is positive, so the expression is negative.

4. When z > 1 and x > 4: In this case, both factors are positive, so the expression is positive.

Therefore, the solution to the inequality is:

(z-1)^2(x-4) < 0 when z > 1 and x < 4.