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24 May 2017, 15:19
Kudos
Bookmarks
Going thru the beginning chapters from GMAT Math book v3, it reads:
\(\sqrt{x^2}\) = |x| and
when x<=0 then \(\sqrt{x^2}\) = -x and
when x>= 0 then \(\sqrt{x^2}\) = x.
My Math is rusty but don't you have to square both sides in order to remove the modulus? Pardon my ignorance on the topic. Maybe someone could help me understand the concept?
p.s: I did search for this question before I posted but the search yielded no results due to too many common parameters provided.
\(\sqrt{x^2}\) = |x| and
when x<=0 then \(\sqrt{x^2}\) = -x and
when x>= 0 then \(\sqrt{x^2}\) = x.
My Math is rusty but don't you have to square both sides in order to remove the modulus? Pardon my ignorance on the topic. Maybe someone could help me understand the concept?
p.s: I did search for this question before I posted but the search yielded no results due to too many common parameters provided.
24 May 2017, 19:01
Kudos
Bookmarks
Look at it this way,
\((-2)^2=4\)
\((2)^2=4\)
Hence applying the reverse
\(√4 =2 or -2\)
and 2 and -2 can be collectively referred as |2|
Thus it follows
\(x^2 = |x|\)and
when \(x<=0\)then \(x^2−−√x2 = -x\) and
when \(x>= 0\)then \(x^2−−√x2 = x\).
This is a very powerful concept, used in multiple questions you will see on this forum. You can check the absolute value/modulus tags for this
https://gmatclub.com/forum/search.php?s ... &tag_id=37
\((-2)^2=4\)
\((2)^2=4\)
Hence applying the reverse
\(√4 =2 or -2\)
and 2 and -2 can be collectively referred as |2|
Thus it follows
\(x^2 = |x|\)and
when \(x<=0\)then \(x^2−−√x2 = -x\) and
when \(x>= 0\)then \(x^2−−√x2 = x\).
This is a very powerful concept, used in multiple questions you will see on this forum. You can check the absolute value/modulus tags for this
https://gmatclub.com/forum/search.php?s ... &tag_id=37
25 May 2017, 15:47
Kudos
Bookmarks
Tan2017
Look at it this way,
...
Thus it follows
\(x^2 = |x|\)and
when \(x<=0\)then \(x^2−−√x2 = -x\) and
when \(x>= 0\)then \(x^2−−√x2 = x\).
...
...
Thus it follows
\(x^2 = |x|\)and
when \(x<=0\)then \(x^2−−√x2 = -x\) and
when \(x>= 0\)then \(x^2−−√x2 = x\).
...
I followed you until \(x^2 = |x|\) ... LOL. I am not sure I understood what followed after. Could you dumb it down a notch for me, please?
