comperr-like Impossible Math: The Elephant and The Mosquito

[unreality]

Does the weight of an elephant equal the weight of the mosquito?

Let x be the weight of the elephant, y be the weight of the mosquito. Call the sum of the two weights 2v, then x+y=2v

From this equation we can obtain two more:

x - 2v = -y

and

x = -y + 2v

multiply:

x^2 - 2vx = y^2 - 2vy

add v^2:

x^2 - 2vx + v^2 = y^2 - 2vy + v^2

OR

(x-v)^2 = (y-v)^2

take square roots:

(x-v) = (y-v)

x = y

The elephant's weight equals the mosquitoes.

What is wrong here?

[Guest]

when you take the square root you ignore an answer to the problem

[Guest]

(x-v)^2 = (y-v)^2

take square roots:

(x-v) = (y-v)

Mathematically when you take the square root of both sides you need a plus or minus on at leat one side:

(x-v) = ±(y-v)

The minus route gives you x + y = 2v again. Obviously you should choose to use the minus out of the plus or minus because anyone would assume they cannot be the same mass, yet you get back to your original equation and realize you are just wasting your time like I just realized.

[unreality]

good job! that problem can get confusing.