Can X=2 and X=-2 at the same time?

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The discussion centers on the mathematical concept of square roots and the implications of assigning multiple values to a variable. It is established that while the square root of 1 can yield both 1 and -1, a variable like X cannot simultaneously represent both values in the same equation. The participants clarify that when solving equations, one must choose a single value for X to maintain logical consistency. The confusion arises from misunderstanding the nature of square roots and the principle that an equation can have multiple solutions, but each instance must adhere to a single value for the variable in question. Ultimately, the conversation emphasizes the importance of clarity in mathematical definitions and operations.
  • #31


ahh but root uses a double o and all the letters are on the same line ... its just more efficient haha
 
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  • #32


It may be more efficient but it's also ambiguous. We could use "root" to represent any nth root whereas "sqrt" specifically denotes the squareroot.
 
  • #33


also true
 
  • #34


so (sqrt 1 - sqrt 1) is different to
x=sqrt 1
x-x
 
  • #35


chalky00 said:
so (sqrt 1 - sqrt 1) is different to
x=sqrt 1
x-x
(sqrt 1 - sqrt 1) has 4 possible solutions.
 
  • #36


chalky00 said:
so (sqrt 1 - sqrt 1) is different to
x=sqrt 1
x-x

No! Hopefully without confusing you too much, if we let x = \sqrt{1} then x=1 because the \sqrt operation retrieves the principal (positive) square root. However, if x is a number such that x^2 = 1 then x=1 or x=-1. Now, using this second definition of x, once we choose a value for x we need to stick with it. We can't have x = 1 and x = -1 at the same time because this would violate the law of non-contradiction and you're already assuming that 1 = -1.
 
  • #37


Stop feeding the troll (OP)!
 

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