# $2 + 2 = 5$ (Fake proof, or ?) [duplicate]

Basically, there is no error in the following steps(as it seems), but there is some error due to which 2 + 2 = 5. What is it?

                      -20 = -20
16-36 = 25-45
16-36+(81/4) = 25-45+(81/4)
(4^2)-(2*4*9/2)+((9/2)^2) = (5^2)-(2*5*(9/2))+((9/2)^2)
(4-(9/2))^2 = (5-(9/2))^2
4-(9/2) = 5-(9/2)
4 = 5
2+2 = 5


## marked as duplicate by user21820, Jonas Meyer, user91500, Claude Leibovici, Chris GodsilApr 20 '17 at 12:25

• $x^2=y^2$ does not necessarily imply that $x=y$. Not to meantion $(5^2)-(2*5*(9/2))+((9/2)^2)\neq (5+(9/2))^2$ anyways. – user12345 Apr 19 '17 at 16:35
• You've gotten $(4-\frac92)^2=(5-\frac 92)^2$ which isn't strange – kingW3 Apr 19 '17 at 16:35
• Taking roots on both sides of $(4-(9/2))^2=(5-(9/2))^2$ you get $|4-(9/2)|=|5-(9/2)|$. The rest should be obvious. – mlc Apr 19 '17 at 16:38