Essentially the question asks if x^3 = [(x + 1)^3] then find all real solutions of x. The square brackets in this case represent the fractional part of the number they enclose.
So far I have figured out that [z] is the number minus the largest integer smaller than itself. I have no idea how to go about finding all real solutions. Any help would be appreciated
Fractional part - Wikipedia, the free encyclopedia
I'm finding it hard to say
NO! He is trying to say that is equal to the fractional part of .Are you trying to say that your question is:
First, notice that that the "fractional part" of any number lies between 0 and 1. That means that whatever x is is between 0 and 1 and then x itself is between 0 and 1. That, in turn, means that x+1 is between 1 and 2 so that is between 1 and 8.
I think the most direct way to do this is to look at each possiblility in turn:
Then it would become:
If "rt21" means "square root of 21", then, yes, that is a solution. Of course, you should check that any "purported" solution is, in fact, a solution.
A more general method would be to look at where b is an integer from 1 to b. That gives which, by the quadratic formula, has solutions .