◆ ILLEGAL MATHEMATICS ◆
[tex]we \: know \: that \:, \\ \\ {x}^{2} = x + x + x + x + x + ...(x \: times) \\ \\ now \: , \: take \: derivative \: of \: both \: sides \: , \\ \\ [/tex]
We get ,
2x = 1 + 1 + 1 + 1 + ....( x times )
Therefore ,
2x = x ( for all values of x )
Putting x = 1
We get ,
2 = 1 or 1 = 2
Hence , proved.
Although ,
The way we took the derivative wasn't correct , as it's not just a simple linear Equation ,
x² = x + x + x + x + ....(x times) = x(x)
Correctly taking derivative ,
We get , 2x = x(1) + x(1)
Or 2x = 2x only ,
which is truly correct :)
