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**Frublox****Member**- Registered: 2012-12-19
- Posts: 1

Got this problem on a test:

____

12 + √2x-1 = 4

Okay, so then I subtract 12 from both sides:

____

√2x-1 = -8

2x - 1 = 64 I then square both sides...

2x = 65 Add 1 to each side

x = 65/2 Divide both sides by two.

However, that answer doesn't work. Are there simply no solutions, then?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi Frublox;

That is correct, there are no solutions. Not every equation is a true statement. You always check the validity of your answer by plugging into the original equation.

Please go here:

**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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,427

hi Frublox

That answer is the solution to

-12 + √(2x-1) = -4

When you square you cannot help but introduce 'solutions' to this alternative equation as well so you were right to check the value you had.

Bob

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: 15,544

Even when you got √2x-1 = -8 you could've said that there are no solutions, because a square root of a positive number is always positive...

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Hi;

Yes, it always takes the principal value.

**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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