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What is wrong with the following algebraic statements:?
X = -2
X^2 = 4
✓(X^2) = ✓4
X = 2
Therefore -2 = 2
I know the square root of 4 is both 2 and -2, but the ✓ symbol is taken to mean only the positive root.
3 Answers
- PopeLv 73 months agoFavourite answer
The trouble lies in going from the third line to the fourth. There it is implied that √(X²) is equivalent to X. That is not correct.
√(X²) = |X|
- ignoramusLv 73 months ago
No.
The convention is that ✓4 is taken to mean the PRINCIPAL root (i.e. the positive root) because that is often the most useful (or the most likely), according to context. But it is axiomatic that the negative root is sometimes more appropriate, and then -2 will be selected. It saves a lot of messing about with the awkward +/- sign in front of the ✓ sign.
Many nonsense results can be "proved" by misusing it as you have done. However, it does not make them true.
Your fourth line is taken out of context. You start off by DEFINING
x = -2, so you error is in re-defining it as +2. You know that it does not agree with the first line.
