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Basic algebra question

  • Thread starter LiHJ
  • Start date
  • #1
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<< Mentor Note -- OP has been advised to type their questions into the forum next time, instead of inserting images >>

1. Homework Statement

Dear Mentors and PF helpers,

I have a question from today's lesson.

image.jpg


Homework Equations




The Attempt at a Solution



Is 1) and 2) both acceptable? If only of of them is acceptable, is there any reason why?

Thanks for your time
 
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Answers and Replies

  • #2
RUber
Homework Helper
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344
Only 2.
The ## \sqrt{} ## implies that it only returns the positive square root of a number. That is why you will often see ##\pm \sqrt{} ## in formulas.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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934
For x any real number, [itex]\sqrt{x^2}= |x|[/itex], NOT [itex]\sqrt{x}= x[/itex]

That is easily seen by taking x to be any negative number, say x= -2. In that case, [itex]x^2= (-2)^2= 4[/itex] and [itex]\sqrt{x^2}= \sqrt{4}= 2[/itex], NOT -2.
 
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  • #4
RUber
Homework Helper
1,687
344
However, if you know something about x, like it is positive, then you may use the notation in (1) .
Also, if you have ##y = x^2##, then ##x = \pm \sqrt{y}##.
 

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