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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!
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#13 2012-07-30 02:48:19
- anonimnystefy
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Re: Equation Involving Radicals
Have a nice day, too.
By the way, cute avatar 
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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
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.
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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!
Last edited by 295Ja (2012-12-03 23:13:02)
#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!
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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.