# Question #5003d

##### 2 Answers

I am not sure if I got the meaning of your question right but I'll try anyway:

Rearranging:

To solve this cubic equation I used the Cardano-Tartaglia formula that you can find in most texts or on the internet such as in Wikipedia:

I supposed that you needed only real roots so I neglected the ones which are complex numbers.

You have only one real root (an irrational number) given as:

You can check it by substituting in:

Probably there are simpler techniques but I do not know. Hope it helped.

There is no value of

By "greatest integer function of *ceiling of #t#* or

*the ceiling function*.

For every finite interval chosen as it's domain, the ceiling function and it's square

where

The integral of any step function is simply the sum of the lengths of all intervals multiplied by their respective constants:

Now, the function

where

It's integral is, observing that all intervals of the form

Now, your question also gives us the condition that

Wich means:

Now, the sum of the first

So,

With the additional condition given to us by the question:

Finding the solution to this equation is not simple. But noticing that the left side behaves itself similarly to a

Consider the left side equation for

The right hand side:

So even where the function at the left side grows at it's slowest, the left side of the equation is greater than the right side. So, for

Another way of thinking about this problem is graphing the integral. For