Find Positive Numbers

Status
Not open for further replies.
harpazo

harpazo

Full Member
Joined
Jan 31, 2013
Messages
891
For what positive numbers will the cube of a number be less the number?

Solution:

x^3 < x
x^3 - x < 0
x(x^2 - 1) < 0
x (x - 1) (x + 1) < 0

Is this correct thus far?
 
Otis said:
That's how I would start, for an algebraic approach.

(There are other methods, some don't even require algebra.)

?
Click to expand...

Solution:

x^3 < x
x^3 - x < 0
x(x^2 - 1) < 0
x (x - 1) (x + 1) < 0

On the number line we write:

<----(-1)--------(0)---------(1)-------->

When x = -2, we get
-8 < -2. True statement.

When x = -0.5, we get
-0.125 < -0.5. True statement.

When x = 0.5, we get
0.125 < -2. False statement.

When x = 2, we get 8 < 2.
False statement.

Solution: (-00, -1) U (-1, 0).

Yes?
 
harpazo said:
... -8 < -2. True statement.
... -0.125 < -0.5. True statement.
... 0.125 < -2. False statement.
... 8 < 2. False statement.
... Yes?
Click to expand...
No. Please double-check your substitutions, evaluations, conclusions, and typing above.

Have you been checking your work, before posting? I'm beginning to wonder because some of the math errors and typos in your threads are still obvious. My hope is that you can prevent much of that, by double-checking your work as you go.

?
 
Otis said:
No. Please double-check your substitutions, evaluations, conclusions, and typing above.

Have you been checking your work, before posting? I'm beginning to wonder because some of the math errors and typos in your threads are still obvious. My hope is that you can prevent much of that, by double-checking your work as you go.

?
Click to expand...

After reworking the problem, my new interval answer is (-00, -1) U (0, 1).
 
Status
Not open for further replies.
Top