Mathematical Puzzle #3

 

Welcome to our "Mathematical Puzzle" Series!

Another mind-boggling question for you! 

Find the below proof of the fact that 4=5.

Start from

${\displaystyle -20=-20}$

Write this as

${\displaystyle 25-45=16-36}$

Rewrite as

${\displaystyle 5^{2}-5\times 9=4^{2}-4\times 9}$

Add 81/4 on both sides:

${\displaystyle 5^{2}-5\times 9+{\frac {81}{4}}=4^{2}-4\times 9+{\frac {81}{4}}}$

These are perfect squares:

${\displaystyle \left(5-{\frac {9}{2}}\right)^{2}=\left(4-{\frac {9}{2}}\right)^{2}}$

Take the square root of both sides:

${\displaystyle 5-{\frac {9}{2}}=4-{\frac {9}{2}}}$

Add 9/2 on both sides:

${\displaystyle 5=4}$

You & I know- this is obviously ambiguous!

Why not crack the mistake then?!

 Exciting Awards waiting for you there! 

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