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## Question

Being the math crazed maniac I was in school, one of my teachers challenged me to prove that 1=2.

Ok, so he said I would fail if I could not prove it....

3 months later I came upwith the solution....

Where is the Flaw?

A=B

A^2 = AB

A^2 - B^2 = AB - B^2

(A+B)(A-B) = B(A-B)

A+B = B

2B = B

2=1

What I did each step: (sorry forum not conducive to spaces)

A=B - Given

A^2 = AB - Multiplicative Property of Equality (A)

A^2 - B^2 = AB - B^2 - Additive Property of Equality (-B^2)

(A+B)(A-B) = B(A-B) - Evaluation

A+B = B - Reduction

2B = B - Substitution and Addition (since first statement say a=b)

2=1 - Reduction (by B)

The "^" means to the power of.

A-B = 0

## 3 answers to this question

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A=B

A^2 = AB

A^2 - B^2 = AB - B^2

(A+B)(A-B) = B(A-B)

A+B = B

2B = B

2=1

If A=B ; A-B=0

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Being the math crazed maniac I was in school, one of my teachers challenged me to prove that 1=2.

Ok, so he said I would fail if I could not prove it....

3 months later I came upwith the solution....

Where is the Flaw?

A=B

A^2 = AB

A^2 - B^2 = AB - B^2

(A+B)(A-B) = B(A-B)

A+B = B

2B = B

2=1

What I did each step: (sorry forum not conducive to spaces)

A=B - Given

A^2 = AB - Multiplicative Property of Equality (A)

A^2 - B^2 = AB - B^2 - Additive Property of Equality (-B^2)

(A+B)(A-B) = B(A-B) - Evaluation

A+B = B - Reduction

2B = B - Substitution and Addition (since first statement say a=b)

2=1 - Reduction (by B)

The "^" means to the power of.

A-B = 0

You are dividing by zero.

(A+B)(A-B) = B(A-B)

You then divide by A-B. And if A=B, then A-B is zero.

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What I did each step: (sorry forum not conducive to spaces)

A=B - Given

A^2 = AB - Multiplicative Property of Equality (A)

A^2 - B^2 = AB - B^2 - Additive Property of Equality (-B^2)

(A+B)(A-B) = B(A-B) - Evaluation

A+B = B - Reduction

2B = B - Substitution and Addition (since first statement say a=b)

2=1 - Reduction (by B)

The "^" means to the power of.

spaces can be kept in code tags ... like this ...

```A=B								   - Given
A^2 = AB								   - Multiplicative Property of Equality (A)
A^2 - B^2 = AB - B^2						   - Additive Property of Equality (-B^2)
(A+B)(A-B) = B(A-B)							   - Evaluation
A+B = B								   - Reduction
2B = B								   - Substitution and Addition (since first statement say a=b)
2=1								   - Reduction (by B)[/code]

"power of" can be easily used as "super-script" ... eg. A[sup]2[/sup] = AB

both code and super-script are buttons when you write posts

and I almost forgot ... already posted in a few variations ... check this

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