Mathematics is a subject of numbers. This field can go to great heights, but it will never ever say that 2 different numbers are equal. In this article, I will show how you can prove that 1 = 2 and then how to destroy this seemingly irrefutable evidence.
First will take 2 quadratic equations: x² + 5x + 6 = 0 and 2x² + 10x + 12 = 0. We know that these two equation could be true because the second equation is just twice the first equation and so we are basically multiplying 2 on both sides of the equation as 2 x 0 = 0. Now let’s see what follows:
What is this conclusion? 1 = 2? How is this possible? These are the questions that are probably going through all of your minds right now. However, I’m going to show you where a cleverly concealed ‘mistake’ can be made.
In the second part of problem, where we equate the two equations together, we push the (x+3) and (x+2) to the right hand side of the equation. Here is where the trouble arises. If we want the quadratic equation to be true, then the product of (x+3) and (x+2) must be equal to zero. If that is true, then either (x+3) or (x+2) must be equal to zero. And if any one of them is zero, then we cannot push it to the other side because we cannot divide any number by zero! This is one of the fundamental rules of mathematics and one cannot simply ignore it! This is why we cannot use this method and state that 1 = 2!
There is another way we can show that 1=2 following the same principle:
Over here, the place we are dividing by 0 is in line 4. As x=y, x-y=0. So, we cannot cancel out x-y in the numerator and denominator as you cannot divide anything by 0.
With the first method, we can essentially prove any number to be equal to another one because we are only multiplying 0 with a different number. So from next time, remember that you cannot divide anything by zero!
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