the absolute value of X to the square is equal to 144

[hunter23]

I just dont understand this problem..

the absolute value of X to the square is equal to 144,
it has four solutions for X, but I dont even know where to start
can anyone help me here?

 

[galactus]

\(\displaystyle \L\\|x^{2}|-144=0\)

This is

\(\displaystyle \L\\-x^{2}-144=0\) and \(\displaystyle \L\\x^{2}-144=0?.\)

Now solve for your 4 solutions.

 

[pka]

Re: Math Help

the absolute value of X to the square is equal to 144, it has four solutions for X,

Someone is confused about that. It is not true!

\(\displaystyle \left| X \right|^2 = 144 \to \;X^2 = 144\) there are only two solutions for X.

If it were \(\displaystyle \left| X \right|^4 = 144 \to \;X^4 = 144\) now there are four solutions: two real and two complex.

Note that for any integer n, \(\displaystyle \left| X \right|^n = \left| {X^n } \right|\)

 

[stapel]

the absolute value of X to the square is equal to 144

Does the above mean "|x²|", "|x|²", or something else?

Did you attempt to translate the original expression from some language other than English? Would it be possible to post the actual mathematical characters? ("To the square" is non-standard English, and the standard verbiage would have been covered extensively in an English-language class, is why I ask.)

Thank you.

Eliz.

 

[hunter23]

the absolute value of X to the square is equal to 144

Does the above mean "|x²|", "|x|²", or something else?

Did you attempt to translate the original expression from some language other than English? Would it be possible to post the actual mathematical characters? ("To the square" is non-standard English, and the standard verbiage would have been covered extensively in an English-language class, is why I ask.)

Thank you.

Eliz.

The exponent "2" would go inside the absolute value
and yeah..my teacher speaks better spanish than english
"to the square" is what he uses
And I dont know how to type the mathermatical characters in this keyboard..thats why I had to describe the problem instead of typing it out.

 

[pka]

The exponent "2" would go inside the absolute value
And I dont know how to type the mathermatical characters in this keyboard..thats why I had to describe the problem instead of typing it out.

Please note that if n is even, it does not matter.
Still there are not four solutions to the problem.

You can use TeX to get the mathermatical characters. Go to 'Forum Help' at the top of the page. There are links to using LaTeX.

 

[hunter23]

The exponent "2" would go inside the absolute value
And I dont know how to type the mathermatical characters in this keyboard..thats why I had to describe the problem instead of typing it out.

Please note that if n is even, it does not matter.

what do you mean by "n"?

 

[galactus]

I must've misinterpreted then.

\(\displaystyle \L\\-x^{2}-144=0\), x=-12i and 12i

\(\displaystyle \L\\x^{2}-144=0\), x=-12 and 12

I thought maybe that's what they were getting at.

 

[pka]

I must've misinterpreted then.

\(\displaystyle \L\\-x^{2}-144=0\), x=-12i and 12i

\(\displaystyle \L\\x^{2}-144=0\), x=-12 and 12

I thought maybe that's what they were getting at.

By George, I think you have it! That must be what is meant.
However, I think it is a misuse of notation.
Here is why: \(\displaystyle - x^2 \le 0\;\& \;\left| {x^2 } \right| \ge 0\).
I now have more objections. With that interpretation there are infinitely many solutions.
For any t, \(\displaystyle 12\left[ {\cos (t) + i\sin (t)} \right]\) is also a solution.

 

[hunter23]

I am very grateful for your help.
Thank you very much.