- #1
mathlover1
- 8
- 0
Somebody find the mistake here:
[tex]
1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{(-1)^2}=-1 \Rightarrow 1=-1
[/tex]
1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{(-1)^2}=-1 \Rightarrow 1=-1
[/tex]
DaveC426913 said:The root of 1 is 1, not -1.
mathlover1 said:yes it's -1 because (-1)^2=1 from the definition ;)
mathlover1 said:Well-done Njama, your answer is the correct one.
Not true.Borek said:Square root of 1 is not 1, it is either 1 or -1.
Not true.mathlover1 said:yes it's -1 because (-1)^2=1 from the definition ;)
True! [tex]\sqrt{x}[/itex], as a real valued function, must have only one value for each x and it is defined as "the positive number y such that [itex]y^2= x[/itex]"njama said:The error is here
[tex]
\sqrt{(-1)^2} \neq -1
[/tex]
[tex]\sqrt{(-1)^2} = |-1|=1[/tex]
Then why did you deny it in your post quoted above?mathlover1 said:Well-done Njama, your answer is the correct one.
This may seem counterintuitive, but it is possible for 1 to equal -1 in certain mathematical equations. In this case, the statement "1=-1" is a false statement, as it goes against the basic principles of arithmetic.
The mistake in this equation is that the equals sign is being used incorrectly. The equals sign is typically used to show that two quantities are equal, but in this case, it is being used to assign a value. This is incorrect, as 1 and -1 are not equal values.
No, this equation cannot be solved as it is a false statement. There is no solution that can make 1 equal to -1.
No, there is no scenario in mathematics where 1 can equal -1. In order for an equation to be true, it must follow the rules of mathematics, and this equation does not.
To avoid making this mistake, it is important to have a clear understanding of basic arithmetic principles. Remember that the equals sign should be used to show that two quantities are equal, not to assign a value. Double-checking equations and calculations can also help catch any mistakes before they are made.