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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
Next: 3 equals 4?
