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4 is equal to 6?


We start with the following equality:

-24 = -24

We wrote the number -24 in two different ways:

16 - 40 = 36 - 60

The numbers 16, 40, 36 and 60 can be written as follows:

4x4 - 2x4x5 = 6x6 - 2x6x5

We can add 25 on both sides of the equation without changing it:

4x4 - 2x4x5 + 5x5 = 6x6 - 2x6x5 + 5x5

Now we see that on both the left and right sides we have a squared binomial (the first squared term minus twice the product of the two terms plus the second squared)

(4 - 5)2 = (6 - 5)2

Eliminating the square on both sides of the equation gives us:

4 - 5 = 6 - 5

Finally, by adding 5 on both sides, we get the result:

4 = 6

Obviously this demonstration has an error because we all know that 4 is not equal to 6 (or does anyone have any questions?). Click below to find out what the error is:

In this demonstration comes a stage where we have:

(4-5)2 = (6-5)2

According to the demonstration, the next step is:

Take the square root on both sides, obtaining:

4-5 = 6-5

There is the mistake !!!

It is wrong because SQUARE ROOT of a number SQUARED is equal to MODULE of this number. So the correct would be:

| 4-5 | = | 6-5 |

| -1| = | 1 |

1 = 1

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