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#1 2012-07-29 23:57:25

295Ja
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Equation Involving Radicals

Hello! I'm here again. Please teach me how to solve equation like this one:
    sqrt(2x+3)-sqrt(x-2)=sqrt(x+1)                          * Note: sqrt- Square root of

What makes it hard for me to solve the above equation is that it has 3 terms with radical expression.
If it only has one or two radical expression I could easily eliminate the radicals from the equation after isolating it
then go on with solving the equation that arise.
But suppose I have more than 2 terms having radical expression(like on my given problem), how could I eliminate the radicals?

Thank you in advance!smile

#2 2012-07-30 00:02:22

bobbym
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Re: Equation Involving Radicals

Hi 295Ja;

Did you first try graphing the equation?

http://www.mathsisfun.com/graph/functio … amp;ymax=8


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-07-30 00:08:39

295Ja
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Re: Equation Involving Radicals

I have not try to graph it.

#4 2012-07-30 00:13:36

bobbym
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Re: Equation Involving Radicals

Hi;

That equation may not be solveable by algebraic methods. Very few types of equations are. Basically we can solve quadratics, cubics and quartics using algebra. After that it is usually not possible.

Do not get stuck on one idea when doing math. From the graph you can immediately see that one root is x = 3. This is verified by plugging in.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-07-30 00:16:38

295Ja
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Re: Equation Involving Radicals

Thank you! smile

#6 2012-07-30 00:25:33

bobbym
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Re: Equation Involving Radicals

Hi;

Looking at the graph I am not too optimistic that can be solved using algebra. Does that graph look like a polynomial? Of course not.
There are numerical methods for such problems. But first you always graph!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2012-07-30 00:32:07

295Ja
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Re: Equation Involving Radicals

I'll follow your advice. smile
Thanks again!

#8 2012-07-30 00:42:56

bobbym
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Re: Equation Involving Radicals

Hi 295Ja;

I will look for another answer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2012-07-30 01:14:01

anonimnystefy
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Re: Equation Involving Radicals

Hi


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10 2012-07-30 01:35:11

295Ja
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Re: Equation Involving Radicals

Thank you anonimnystefy! smile

Just curious, what is now the time in your place? By the way, it's now 11:38 pm here.smile

#11 2012-07-30 01:37:05

anonimnystefy
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Re: Equation Involving Radicals

17:36pm here in Serbia.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#12 2012-07-30 01:56:23

295Ja
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Re: Equation Involving Radicals

Thank you for the reply. I forgot to tell you that I'm from the Philippines. Until next time! Have a nice day!smile

#13 2012-07-30 02:48:19

anonimnystefy
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Re: Equation Involving Radicals

Have a nice day, too. smile

By the way, cute avatar big_smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#14 2012-07-30 04:08:31

bob bundy
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Re: Equation Involving Radicals

hi 295Ja

This method will always (I think) work for questions like this.  Just one thing to watch out for:  it will give genuine solutions; it may also throw up answers that are not solutions.  So you have to check each answer you get.



square each side



simplify and re-arrange



square again



simplfy



factorise



Now why is it necessary to check these?

consider a simple example.



This quadratic has two solutions     y = -5 and y = 5.

The act of squaring has made an extra answer.

So could x = 3 be a solution?



So x = 3 works.

Could x = -2 be a solution?



where i is the square root of minus 1.  (if you've not yet met complex numbers just reject -2 as you 'cannot square root a negative')

So there is one answer, x = 3

Bob

ps.  Stefy;  My turn.



That should be



smile

You'll find this then leads to the same quadratic as mine.


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#15 2012-07-30 05:24:26

anonimnystefy
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Re: Equation Involving Radicals

Hi Bob

True. Thanks for the correction. smile

Btw, our teacher told us it is better if we make the irational equation so that all signs in front of radicals are positive. That is why I transferted one term to the other side.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#16 2012-07-30 06:31:48

bob bundy
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Re: Equation Involving Radicals

hi Stefy,

Did your teacher say why?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#17 2012-07-30 13:23:18

295Ja
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Re: Equation Involving Radicals

It's now 11:24 in the morning here.  Last night, something went wrong with the internet connection due to the typhoon so only now was I able to see the other replies.

anonimnystefy and bob bundy: I tried to solve the problem following your ideas. I got it now.

Thanks again anonimnystefy,bob bundy and bobbym!
Till next time!smile

Last edited by 295Ja (2012-12-03 23:13:02)

#18 2012-07-30 16:50:26

bob bundy
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Re: Equation Involving Radicals

hi 295Ja

You're Welcome.

Glad you survived the storm.  smile  Does that happen very often?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#19 2012-07-30 17:47:11

295Ja
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Re: Equation Involving Radicals

Hi bob bundy!

An average of 20 storms and/or typhoons per year enters the Philippines usually from July through October.

By the way, I'm now moving on to solving problems about inequalities then 2 dimensional coordinate system.
Glad I could ask problems I can't solve here! smile

Last edited by 295Ja (2012-12-03 22:53:52)

#20 2012-07-30 17:49:47

anonimnystefy
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Re: Equation Involving Radicals

Hi Bob

Of course he said. But I forgot. I think it is so that we make sure neither side is negative.

Hi 295Ja

You're welcome. Hope everything else was okay during the storm.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#21 2012-07-30 22:18:17

bob bundy
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Re: Equation Involving Radicals

hi Stefy







and







I realise it will be hard for you to believe it but, sometimes, even teachers talk a load of rubbish.  smile

aude sapere  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#22 2012-07-30 23:06:18

anonimnystefy
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Re: Equation Involving Radicals

I never said tachers new everything. It just seems logical. Even our book says it is better if we did itbthat way, so that we are sure both sides are positive.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#23 2012-07-31 12:42:35

bobbym
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Re: Equation Involving Radicals

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#24 2012-07-31 19:25:04

anonimnystefy
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Re: Equation Involving Radicals

Hi bobbym

Nice one. But I think you should explain why -2 isn't a solution.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#25 2012-08-01 00:25:01

bobbym
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Re: Equation Involving Radicals

Hi;

But I think you should explain why -2 isn't a solution.

Spurious solutions are detected by plugging in. -2 does not work.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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