1=sqrt(1)=sqrt((-1)*(-1))=-1.. so 1=-1 ...how is this possible?

Question

whats wrong in this proof..
using this we can make x=-x...
this is a maths related question

Answer 1

sqrt(1)= + or - 1
becouse every no can make by multipling - values also

Answer 2

Just because x^2=y^2 does not mean that x=y!!

(-1)^2=1=1^2, this does not mean that -1=1.

The problem with you logic is that √(x^2) is not x, but |x|. Therefore √(-1•-1)≠-1, but √(-1•-1)=|-1|=1.


The problem that most people have is that √ is not a well defined function from postive numbers to all numbers. It must be restricted to the range of positve numbers (or negative numbers), if you want it to be well defined.

If you have a function f that isn't well defined then for some point a (at least 1) f(a) has at least two values. Call two of these values b and c. Then f(a)=b, and f(a)=c. Thus b=f(a)=c.


Here is an example of such a function. All rational numbers can be written as a ratio of integers m/n. Let f be a function from rational numbers to the integers such that f(m/n)=m•n. Then f(1)=f(1/1)=1•1=1.

But f(1)=f(2/2)=2•2=4.

Does this mean that 1=4? No, because f is not well defined.

Answer 3

The sqrt(-1*-1) is not -1. It's positive 1.

The sqrt(x^2) = the absolute value of x. This is because you multiply first. Two negative numbers multiplied together equal a positive number. The sqrt of a positive is a positive.

If you use the sqrt to undo the ^2, then you have to include a +/-sqrt.

For example x^2 = 4, then x could either be -2 or 2

Answer 4

The problem is the following:

You have assumed that sqrt( a * b ) = sqrt( a ) * sqrt( b )
This is not always true, as you yourself have seen. For this to be true, either a or b must be positive. -1 is not positive, so you cannot say that sqrt( (-1)*(-1) ) = sqrt( -1 ) * sqrt( -1 ) = -1.


Eulercrosser also gave a nice explaination. Looks like most others missed the point though...

Answer 5

Square both sides and you have 1*1 = -1*-1 = 1.

You not proven that 1 = -1 but that 1 = 1.

Instead of wasting you time on nonsense, try learning more mathematics.

Answer 6

-1 has a real root and a complex root denoted by "i", i = sqrt(-1); so u will get your answer easily if u have some knowledge about copmplex roots

Answer 7

compleletly faulty. (-1)*(-1)=1 but -1=1,

its like saying 2*2=4.

it is unlogical.

Answer 8

(-1 * -1) = 1 not -1
a sqrt can never be negative

Answer 9

ok, first thing
sq root of -1 is not 1
there is not defined in real number. it is defined in virtual number which is "i"
and square root of +1 is positive or negative 1, you might have noticed a postive sign and below a negative sign. that is what it is

Answer 10

-1*-1=1
and 1=1