What is wrong with this maths logic?

Question

a = b

a² = ab

a² + (a²- 2ab) = ab + (a²- 2ab)

2a² - 2ab = a² - ab

2(a² - ab) = 1(a² - ab)

2 = 1

Answer 1

i think there's something wrong in the 3rd sentence

Answer 2

the logic is wrong because in the 5th line the stuff in ( ) is equal to zero.

Answer 3

In the last step, a² - ab is equal to zero... so you are performing an illegal step when you divide both sides by a² - ab.

Given:

a = b

Multiplying both sides by the same value a:

a² = ab

Adding the same amount to both sides:

a² + (a²- 2ab) = ab + (a²- 2ab)

Simplifying/canceling:

2a² - 2ab = a² - ab

Distributing out a common 2:

2(a² - ab) = 1(a² - ab)

Dividing both sides by (a² - ab) <-- not legal because that is a division by 0.

2 = 1

Answer 4

Before the last line, you cannot divide by (a² - ab), because (a² - ab)=0 (see the second line).

Answer 5

a squared does not equal ab. At least I think it doesn't anyway!

Please answer mine! I tried!

http://malaysia.answers.yahoo.com/questi...

Answer 6

If we have got equation 2x=x, it does not mean that 2=1!

It just means, that the variable x=0.

In your equation u have got variables a and b

And in result (a^2-ab)=0 => a=b

Nothing more.