-1/1 = 1/-1
⇒ √(-1/1) = √(1/-1) (taking the square root of both sides)
⇒ √(-1)/√1 = √1/√(-1)
⇒ i/1 = 1/i
⇒ i/2 = 1/(2i)
⇒ i/2 + 3/(2i)= 1/(2i) + 3/(2i)
⇒ i(i/2 + 3/(2i))= i(1/(2i) + 3/(2i))
⇒ i²/2 + (3i)/(2i)= i/(2i) + (3i)/(2i)
⇒ (-1)/2 + 3/2 = 1/2 + 3/2
⇒ 1=2

Can you spot the flaw in the above proof?

Even  for real numbers a=b does not imply sqrt(a)=sqrt(b),

we should cautiously write sqrt(a)= ±sqrt(b) and explore both cases,

Therefore the 2nd  line should be amended , inserting ± on one of the sides,

Posted by Ady TZIDON on 2012-09-27 16:47:27