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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

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!:)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

Hi 295Ja;

Did you first try graphing the equation?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

I have not try to graph it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Thank you!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

I'll follow your advice.

Thanks again!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

Hi 295Ja;

I will look for another answer.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Thank you anonimnystefy!

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

17:36pm here in Serbia.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Have a nice day, too.

By the way, cute avatar

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,384

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

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi Bob

True. Thanks for the correction.

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.

Here lies the reader who will never open this book. He is forever dead.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,384

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

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

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!:)

*Last edited by 295Ja (2012-12-03 00:13:02)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,384

hi 295Ja

You're Welcome.

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

Bob

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

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

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!

*Last edited by 295Ja (2012-12-02 23:53:52)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

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.

Here lies the reader who will never open this book. He is forever dead.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,384

hi Stefy

and

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

aude sapere

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

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.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Hi bobbym

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

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,460

Hi;

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

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**