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Posted on: Feb 29, '08


 Can You Prove This Wrong..???

Here is another brain-teaser for this weekend...

Can u prove this wrong... 

Prove 3=2?? 

This seems to be an anomaly or whatever u call in mathematics. 

It seems, Ramanujam found it but never disclosed it during his life time and that it has been found from his dairy. 

See this illustration: 

 -6 = -6
  9-15 = 4-10
  adding 25/4 to both sides:
  9-15+25/4 = 4-10+25/4
  Changing the order
  9+25/4-15 = 4+25/4-10
  (this is just like a² + b² - 2a b = (a-b)².)
  Here a1 = 3, b1=5/2 for L.H.S
  and a2 =2, b2=5/2 for R.H.S.
  So it can be expressed as follows:
  (3-5/2)(3-5/2) = (2-5/2)(2-5/2)
  Taking positive square root on both sides:
  3 - 5/2 = 2 - 5/2
  3 = 2 ???????? 

  Can u find out any mistake in the above
..???








OK Folks, 

Thanks for scratching whatever you had to, to get an answer to this one... 

Here is the explanation:
When you take square root, it is always + or -.
Hence, the square roots will be:
 +/-(3-5/2) = +/- (2-5/2)
Here the of left side is equal to the - of the other side.
Thus,
    +(3-5/2) = -(2-5/2) => +(0.5)=-(-0.5)
Therefore,
    3-5/2 = -2+5/2 => 
      3 = -2+5/2+5/2 = -2+5 =+ 3
       So, 3 = 3



Tags: mathematics, quiz, maths, trivia





Comments  [ 12 Comments ] [ Post your comment | Subscribe (?) ]


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King-Bulls-Ring said:
Snehajee, you are right.. the PLUS sign is not displaying in the comment... Grrrrrr....

I have given the answer at the end of the blog, to show the plus and minus...

Mods, please check this bug out...

March 06, '08


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LovelyStars said:
OOps 'plus' sign is coming in the output.
(A plus B) (A minus B) = A^2-B^2

March 05, '08


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LovelyStars said:
Rajaji...one again without getting bias from other comments, I am writing my own. Ofcourse I spent some time in identifying the mistake in this process.

Until the step
So it can be expressed as follows:
(3-5/2)(3-5/2) = (2-5/2)(2-5/2)..........(1)
Nothing wrong in the process.
The immediate step was wrong. Let me explain now.
In (1), let (3-5/2) = A and (2-5/2) = B
Now (1) can be written as
A^2 = B^2.........(2)
We should not take square roots on both sides, because whatever we do, it should satisfy the following condition
A^2 - B^2 = 0 .........(3)
which is equivalent to
(A B)(A-B)=0

Now substituting A and B values, we get
(1)(0) = 0
That means as long as one factor is zero, whatever may be the other factors, the end result is zero and satisfies our initial step
C = C => C-C=0

Hope I haven't confused you.
Sneha

March 05, '08


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LovelyStars said:
Rajaji...one again without getting bias from other comments, I am writing my own. Ofcourse I spent some time in identifying the mistake in this process.

Until the step
So it can be expressed as follows:
(3-5/2)(3-5/2) = (2-5/2)(2-5/2)..........(1)
Nothing wrong in the process.
The immediate step was wrong. Let me explain now.
In (1), let (3-5/2) = A and (2-5/2) = B
Now (1) can be written as
A^2 = B^2.........(2)
We should not take square roots on both sides, because whatever we do, it should satisfy the following condition
A^2 - B^2 = 0 .........(3)
which is equivalent to
(A B)(A-B)=0

Now substituting A and B values, we get
(1)(0) = 0
That means as long as one factor is zero, whatever may be the other factors, the end result is zero and satisfies our initial step
C = C => C-C=0

Hope I haven't confused you.
Sneha

March 05, '08


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sazzyme said:
kaybee i believe when ya changed the order is when something went amiss...

March 02, '08


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chithrajust said:
but of course, i do remember and understand (a-b) formula; and from what i see here, i don't think there is anything wrong!

all the best

March 02, '08


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chithrajust said:
well---------commenting on this post is just an attempt to defy the belief that 'language lovers' are pathetic at math; and commenting is ALL i can do about it; DON'T ask me to solve problems; ha haaaaaaaaa

estranged lad, 'real and rational'? you just need more experience to realize that women are the only 'real rationals' in this world!

and bharathselvan, you're just pushing your luck tooooooooooo far!

March 02, '08


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ASYLUM said:
I don't see any mistake in the above..unfortunately. :(

You ask if 2 x 2 = 4 and -2 x -2 = 4, then why can't 2 = -2?

The square of any number; positive or negative; is ALWAYS a positive. If the squares of two integers are the same, it only means the value of the two integers are the same. Now whether those integers are positive or negative cannot be judged by looking at their square numbers.

The square root of 4 is not always a 2, it could also be a -2. We can never assume by looking at the '4'. And that makes squares unreliable for us to use them to equate, in such a manner.

March 01, '08


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Novacaine said:
*faints* I used to flunk in maths in school... khee khee khee.

February 29, '08


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King-Bulls-Ring said:
Shome,
Thanks for details.. My question is why 'we cannot surely say 2 = -2 when 2x2 = -2 x -2?
I am looking for more precise answer. Let us see anyone else comes up with it.

Rohit,
These are like fillers in the interludes of main episodes of tear-wrenching Mega Serials.
Just to take a break and have a Coffee...
Oooo. COFFEEE.. I better grab my next mug of that wonderful thing on the earth..
see ya..

February 29, '08

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