- #1
Holocene
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Simple math rules seem contradictory... :(
Consider this simple expression:
[tex]x^8 - 16[/tex]
If we wanted to write this expression as the product of two factors, we could start with something simple like this:
[tex]\sqrt{x^8 -16}[/tex] . [tex]\sqrt{x^8 -16}[/tex]
From that, we would simply get this:
[tex](x^4 - 4)(x^4 - 4)[/tex]
This is wrong though, as it does not equal the original expression. Multiplying two negative values will result in a positive value for 16. This is false, as the original exprsssion clearly has a negative value for 16.
So, one of the signs in [tex](x^4 - 4)(x^4 - 4)[/tex] must chnage to a possitive sign.
It just seem to me like, at times, some of the mathematical rules seem contradictory.
Or am I wrong in that you cannot take the individual roots of the terms in an expression?
Anyone information would be greatly appreciated?
Consider this simple expression:
[tex]x^8 - 16[/tex]
If we wanted to write this expression as the product of two factors, we could start with something simple like this:
[tex]\sqrt{x^8 -16}[/tex] . [tex]\sqrt{x^8 -16}[/tex]
From that, we would simply get this:
[tex](x^4 - 4)(x^4 - 4)[/tex]
This is wrong though, as it does not equal the original expression. Multiplying two negative values will result in a positive value for 16. This is false, as the original exprsssion clearly has a negative value for 16.
So, one of the signs in [tex](x^4 - 4)(x^4 - 4)[/tex] must chnage to a possitive sign.
It just seem to me like, at times, some of the mathematical rules seem contradictory.
Or am I wrong in that you cannot take the individual roots of the terms in an expression?
Anyone information would be greatly appreciated?
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