Prove how 1= -1 is wrong?

Question

1=1^2(1 square)
1=+root1 or -root1
1= -root1
squaring both sides
1= -1
how is this possible

Answer 1

1 is not equal to -root1 so your answer was wrong.

Answer 2

The second line is false. Also, when you square both sides 1^2=1 but (-root1)^2=1 not -1.

Answer 3

You have to be consistent when taking the square root. The first step is correct, 1 = 1^2. Your problem is when you take the square root of the first step to get line 2. Each side would have a positive and a negative root. So it's not correct to say that 1 = +SQRT(1) or -SQRT(1). Your second line should be: +/- 1 = +SQRT(1) or -SQRT(1). Each root must be matched up correctly, so that your third step would either be +1=+SQRT(1), or -1=-SQRT(1). Squaring each of those equations, would give the desired result of 1=1.

Answer 4

1=+root1 or -root1

This statement is correct. But notice the word "or." "Or" implies that you must choose one of the two solutions that you have found. But it is clear that 1 does not equal -1 so the correct choice would have to be +root 1 which equals 1.

Answer 5

the square root of 1 have 2 possible answers: 1 and -1.
Just like a simple question:
Do you like boys?
Some would say yes but some would say no or maybe but yes is not equal to no or maybe...
Its just an example of using too much of your imagination to come up with that kind of question.
Now let me as you is 2=3?
2x=3x
if you divide both side by x, 2 will be equal to 3.
explain that..

Answer 6

ok...your last step is erroneous.
the correct thing to do is this:

1=-sqrt(1)
1^2=(-sqrt(1))^2
1=1
remember to square EVERYTHING on one side, including the negative sign. A negative number times a negative number is positive. And hence, the world doesn't come to an end.

Answer 7

Simple, you started with a wrong equation... If you started with
1 = -1, you can not arrive to 1 = 1^2.

Answer 8

-root1 square is 1 not -1...

[-1(1^1/2)]^2= (-1x-1)(1)
=1
Hence it's 1=1 not 1=-1

Answer 9

1 is not = to sqrt[-1]

The sqaure root of any negative number is n imaginary number. This is often denoted by i, or j in some texts.

For example i1 = sqrt[-1]
i2 = sqrt[-4]

Now i^2 = -1 which means (sqrt[-1])^2 = -1
This is different from (-1)^2 which = 1.

Answer 10

it's not possible!
1=1^2 (1squared),
1=(-1)squared=+1
1=+root, but does NOT equal to -root 1
(when there is NO sign before a number, it means the number is POSITIVE(+)!!!))
therefore, 1 does NOT = -1