2 + 2 = 5? Two Plus Two Equals Five?

Two plus Two Equals Five, is it possible?

Two plus two equals five” (“2 + 2 = 5“) is a famous phrase used in George Orwell’s book Nineteen Eighty-Four; therein, it is used as an example of an obviously false dogma one may be required to believe because of political or religious pressures. Orwell’s protagonist, Winston Smith, uses the phrase to wonder if the State might declare “two plus two equals five” as a fact; he ponders whether, if everybody believes it, does that make it true?

Here in India we’ve a famous movie starring Amitabh Bachchan and Shashi Kapoor in the name “Do Aur Do Paanch”, the literal translation of which is two plus two equals five. So what’s the fallacy behind this simple calculation?

Authorities can make you believe something which may be completely baseless.  However, is it mathematically possible to proof: 2 + 2 = 5

Let us give it a shot.

Required to prove, 2+2 = 5?

We all know, 2+2 = 4

2+2
= 4 – 9/2 + 9/2
= √(4 – 9/2)2 + 9/2
= √(16 – 2*4*9/2 + (9/2)2) + 9/2
= √(16 – 36 + (9/2)2) + 9/2
= √(-20 + (9/2)2) + 9/2
= √(25 – 45 + (9/2)2) + 9/2
= √(52) – 2*5*9/2 + (9/2)2) + 9/2
= √(5 – 9/2)2 + 9/2
= 5 – 9/2 + 9/2
= 5
Therefore, 2+2 = 5 (proved)

Oh boy, how’s that possible? Amusing, isn’t it? Let me know if you like this post. If yes, share it on social media with your friends.

Use your grey cells and find out the fallacy. Where’s the mistake in above proof? Put your answers in the comment below.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

4 thoughts to “2 + 2 = 5? Two Plus Two Equals Five?”

  1. Actually {√(16 – 36 + (9/2)²) }cannot be put equal to {√(25) – 2*5*9/2 + (9/2)²) } because if it is so then:
    (4-9/2)² = (5-9/2)²
    Taking sq. root and positive sign on both sides, it gives:
    -1/2 = 1/2
    But taking sq. root and negative sign on left side, it says:
    1/2 = 1/2
    So 2+2=5 is true if we take only one condition which cannot hold here.

    1. You cannot add or subtract in under root like_/16-36 is not equal to – 20 but if we take the root out it will be 4-6 that is – 2….hence 2+2≠5

  2. The falacy lies in the fact that that the square-root of (1/2) square is both plus +1/2 and minus 1/2. if we add minus 1/2 to 9/2 the answer is 4 and not 5 That is all

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