Math Is Fun Forum

Brent

Guest

Equation help?

Hey guys, I was having some trouble with this question.

Solve the equation x^4-2x^2+1=0 for x, where x is real
For this question, do I need to move x to one side? and what does it mean when it says "where x is real"?

Also for this question
solve the inequation (x-4)^2(x+2) less than or equal to 0
Do I expand first, collect the like terms and get x on its own?

If what I have been saying is wrong, could you please show me the working out of how to do it, please?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation help?

Hi Brent;

Welcome to the forum. For the first one use the substitution:

That reduces the equation to

You can now just use the quadratic formula. Or if you can factor well:

Your second one has a missing operator, I think.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Brent

Guest

Re: Equation help?

I don't understand the first part of the first equation. How did you go from y=x^2 to y^2-2y+1=0? Could you show a little more working out please?

I double checked the second equation and that's how it's written in the book .....

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation help?

Can be thought of as

Now just plug into your original equation.

Are you okay with it now?

Is that what it is?

Have you ever seen a quartic before. I am concerned because you do not appear to know what a Real number is. Have you heard of Nine Zulu Queens Ruled China?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Brent

Guest

Re: Equation help?

Thanks I get it now.

Yep, that's what I meant

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation help?

Did you get all the roots to that quartic?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Brent

Guest

Re: Equation help?

yeah I did

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Equation help?

For the second one what are the roots of the inequality if it were an equation?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Equation help?

hi Brent

For inequalities I recommend a sketch of the graph first; in this case

see below for the graph using Maths is Fun function grapher.

You can see from this that the curve crosses or touches the x axis at the points where x-4 = 0 and x + 2 = 0.

So you certainly do not want to expand the equation.  It is already in the most helpful format.

The curve starts below the x axis; crosses at x = -2; goes up to a 'maximum'; turns and just touches at x = + 4; before turning around again and heading off into positive values.

So, when is it less than or equal to zero?

x less than or equal to -2 and at x = 4.

Good morning bobbym,

How are you?  The Sun is shining from a beautiful clear blue sky here today.  So do I go out and spend the day in traffic jams or stay at home and enjoy the garden?

Bob

Last edited by Bob (2011-04-21 20:33:56)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Brent

Guest

Re: Equation help?

Wait, I don't get what you mean
*is slow*

Brent

Guest

Re: Equation help?

oh wait, I take that back. I actually understand it now. XD
Thanks bob bundy

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Equation help?

Hi Brent,

Check this page when you have some free time.
http://www.mathisfunforum.com/viewtopic.php?id=15139
There are some good points that will help you graph functions.