Question

How to Solve? 1/4th root of (x-x^4)≥0
(Clarify: mean 1 over the 4th root of x-x^4)

Answer 1

\[\sqrt[4]{x -x ^{4}}\ge 0\]Correct?

Answer 2

no, its that in the denominator with a 1 on top

Answer 3

First, think about Domain Issues. If \[x \le x^4\], there is no solution in the Real Numbers

Answer 4

\[\frac{ 1 }{ \sqrt[4]{x -x ^{4}} }\ge 0\]Correct?

Answer 5

yes

Answer 6

Now first we must find the domain (restrictions on the variable). Do you know how to do that? What @tkhunny said is not true so don't be influenced by that.

Answer 7

I'm not really sure how to

Answer 8

For example, the denominator cannot be zero and the radicand cannot be negative for even roots, if the solution is to be in the reals. Correct?

Answer 9

Radicand is the expression inside the root sign.

Answer 10

Okay, i understand that

Answer 11

@Studentc14 do you understand?

Answer 12

Good!

Answer 13

Not sure how to respond to that. You call it incorrect when I say it but then repeat it yourself? Please rethink your disclaimer against my correct statement in the beginning.

Answer 14

So then can you tell me what the domain is?

Answer 15

well i understand what it is but i dont know how to go about it with finding it... i know that 1 is a not a solution because that gives you 0

Answer 16

@tkhunny you said that there is no solution in the real numbers but if x = 0.1, for example, would the radicand not be a real number?

Answer 17

if you wouldn't mind, just please ignore each other and help me solve the problem.

Answer 18

Incorrect. Go read it again. I was talking about the Domain, just like you. I was not offering a solution. Please read more carefully, certainly prior to correcting things that don't erquire correction. On the other hand, I do apprecieate your zeal in defending the student.

Answer 19

OK @Studentc14 I'll walk you through the steps, hence guiding you towars the correct solution, without giving away the answers. Alright? Ready?

Answer 20

ok

Answer 21

@Studentc14 - learning to read and understand the writings of others is an important part of your learning. Anyway, I'll leave it to calculusfunctions from here. Good luck.

Answer 22

@tkhunny you said that\[x \le x ^{4}\]has no solution in the reals. Except that it does. For example, if x = 0.1 then\[x \le x ^{4}\]

Answer 23

Not so. You missed the "if" AND you failed to address the orignal problem. Please read the whole statement with reference to the original problem.

Answer 24

@Studentc14 first since the denominator cannot equal zero and the radical is in the denominator,\[x -x ^{4}>0\]Correct?

Answer 25

yes

Answer 26

OK @Studentc14 then we first need to solve this inequality to find the domain. Do you know how to solve this inequality?

Answer 27

not really..

Answer 28

OK first we factor the expression on the left side of the inequality. Can you do that?

Answer 29

no i dont know how to do it with 4th powers

Answer 30

You're over thinking it. It doesn't matter what the powers are. Step on e is always to decide whether there is a greatest common factor. Is there a greatest common factor?

Answer 31

x? then it would be x(1-x^3)

Answer 32

What is the greatest common factor of\[x -x ^{4}\]

Answer 33

Perfect!

Answer 34

So then we have\[x(1-x ^{3})>0\]Correct?

FYI that's exponent 3. With the equation editor on this site, the exponents 3 and 2 look the same. As long as you know that's a 3. OK?

Answer 35

Since we're only interested to find x values in the reals

In other words in which of these interval(s) is\[x(1-x ^{3})>0\]Can you finish that interval line and tell me?