what's wrong with this proof!!!!!?

Question

1=-1

1=root of 1square=root of -1*-1=root of -1square=-1

plz answer
what's wrong with this proof!!!!!!!!!!!!

Answer 1

First of all the square root must be positive, so sqrt(-1*-1) must be positive. Implicit in your proof is the step sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i^2=-1.
However, the property sqrt(ab)=sqrt(a)sqrt(b) only applies to real numbers, above it is being applied to imaginary numbers. So the proof fails for that reason.

Answer 2

Case One:-
The root of the square of 1 = The root of (1)*(1) = The root of the square of 1 = 1.

Case Two:-
The root of the square of -1 = The root of (-1)*(-1) = The root of the square of -1 = 1.

{ The square of a number is always positive!! }

Thus, in a way, you can say that 1 = -1, as far this problem is concerned!!

Answer 3

it is true that the root of 1 can be both 1 or -1 (b/c 1*1=1 and -1*-1=1) however, just because they are both square roots of 1 does not mean they are the same number-the square root of 1 is 1 OR -1. they are different.

Answer 4

The first statement is incomplete:

+/- 1 = sqrt(1)

There are two things that equal the square root of 1. They both have to be stated initially.

Good proofs start with true statements and use true methods to generate other true statements.

1 = 1 (true given)
-1 * -1 = 1 * 1 (true substitution)
sqrt(-1 * -1) = sqrt(1 * 1) (true operation)

Pulling the insides of the square-root operation out, and claiming they are equal is false, and you have shown it. You know that one is not the same as negative one.

Answer 5

You've ignored the notion that square root of 1 is equal to both 1 and -1.

Just because -1 squared = 1, does not imply 1 =-1 squared only.

ie: every table is a 4 legged object does not imply every 4 legged object is a table

Answer 6

-1*-1=1, not -1

Answer 7

u cant take root of -1

Answer 8

simple 1 does not equal -1
Can't have the square root of -1.

Answer 9

If u think thats right, then what about this
1/0=infinity-----1
2/0=infinity----2
Equate 1 & 2
then 1/0=2/0
i.e. 1= 2
Understand the answer by this ex

Answer 10

In your proof square root is not taken on both sides, but not one side.