1.- Suppose we have the following mathematical equation:

a = b

where *to* It can be any positive number.

2.- If we multiply both members of equality by *to*, the validity of the equation is maintained:

to^{2} = ab

3.- The same happens if we add (a² - 2ab) to both sides. In this case, we will have the following equation:

to^{2} + (to^{2} - 2ab) = ab + (a^{2} - 2ab)

4.- Simplifying we have to:

2nd^{2} - 2ab = a^{2} - ab

5.- Now we get a common factor and we have the following:

2a (a - b) = a (a - b)

6.- If we simplify (a - b) we have to:

2nd = a

7.- And if we now divide both terms by the result is:

2 = 1

Which certainly seems a false statement ... **Where have we been wrong?**

#### Solution

The error is subtly hidden in the problem statement. Initially we are told that a = b, so the term we simplify in step 6 (a - b) will be zero. It is clear that we cannot divide by zero to simplify the equation, so this would be the wrong step of our deduction.