One is equal to minus one.

[marco]

1 = √(1)
= √[(−1).(−1)]
= √[(−1)^(2)]
= [(-1)^2)^0,5]
1 = -1

Where is my mistake?

 

[saor]

What did you do in the 4th line?
= [(-1)^2)^0,5]
?

 

[longboy]

1 = √(1)
= √[(−1).(−1)]
= √[(−1)^(2)]
= [(-1)^2)^0,5]
1 = -1

Where is my mistake?

Not listening to your highschool Math teacher.

 

[Hamster]

What did you do in the 4th line?
= [(-1)^2)^0,5]
?

-1^2 = 1 and then if memory serve ^1/2 is the square root or something so √1 = 1

So 1 = 1 and what Eks said ^

 

[saor]

-1^2 = 1 and then if memory serve ^1/2 is the square root or something so √1 = 1

So 1 = 1 and what Eks said ^

Shhh
Was trying to give OP a hard time in case they just reposted this without even understanding it .

 

[marco]

4th line.
Square root and squared cancel out.
(√)^2 or 1/2 X 2 =0
√(9^2) = 9

 

[marco]

Not listening to your highschool Math teacher.

I was one. Tech college N3 + 4

So far nobody understands it. The answer is correct. 1 = -1

 

[Polymathic]

All squares of positive numbers have 2 possible solutions

 

[Hamish McPanji]

I was one. Tech college N3 + 4

So far nobody understands it. The answer is correct. 1 = -1

No wonder the level of maths is, so bad in SA

 

[RedViking]

Need to remove the equal sign.

1-1

Why?

Because

 

[Sinbad]

All squares of positive numbers have 2 possible solutions

Correct. Sqrt(1) = Plus one or minus one.

The assertion is incorrect as you're not performing the same operations completely on both sides of the equation.

 

[marco]

1 = √(1)
= √[(−1).(−1) ....-1 . -1 = + 1
= √[(−1)^(2)] .... -1 . -1 = (-1)^2
= [(-1)^2)^0,5] .... powers cancel
1 = -1

 

[Gordon_R]

You are not the first person to try this false proof:

One Equals Minus One - ProofWiki

The property:
√a×√b=√ab
can only be used when:
a≥0 and b≥0

 

[Polymathic]

Correct. Sqrt(1) = Plus one or minus one.

The assertion is incorrect as you're not performing the same operations completely on both sides of the equation.

Plus the implication from the OP is that 0 = 2 or 0= -2

 

[Sinbad]

Plus the implication from the OP is that 0 = 2 or 0= -2

Next he'll be saying trump = winner

 

[newklear]

(-1 * -1) = 1 but, +1 != -1 following the rules of mathematics.
You can say that: 1 = -1 || +1

 

[Hamish McPanji]

How about this?

5 x 0 = 1,000,000 x 0
5 = 1,000,000 (the x 0 cancel)

Does that work?

 

[newklear]

a = 5
b = 1,000,000

(0 * a) * b = nought

 

[marco]

The calculation method is correct but:
Mathematical rules do not quite allow square roots of negative numbers.

√(−1) would be an imaginary number "i".

√(−9) would simplify to:

√(−1) . √9
= 3i

 

[Hamster]

(-1 * -1) = 1 but, +1 != -1 following the rules of mathematics.
You can say that: 1 = -1 || +1

I'm phone the bank manager tomorrow morning first thing