impossible result

[philllip1882]

i cant for the llfe of me find the flaw with his logic.

somewhere between factoring each polynomial and the step before is wrong. but i see no mistake.

[EventHorizon]

Spoiler

The error happens when he takes the square root of both sides.

(4-9/2)^2 = (-1/2)^2 = (1/2)^2 = (5-9/2)^2

Or more simply...

(-1)^2 = (1)^2, take the square root of both sides gives -1 = 1.  Except it doesn't!

sqrt((-1)^2) = |-1| = |1| = sqrt(1^2)

 

[Martyna]

This is so hard!

[pro]

Spoiler

so you cant say that just because X² = Y², X = Y, that would be theoretically incorrect. X² = Y² implies that X = |Y| where |a|  or mod(a) denotes +/-a. From there we eliminate the absurdity and only consider the solution for the equation that makes sense

 

[bonanova]

Spoiler

His penultimate line evaluates to (-1/2)² = (1/2)² which is correct: 1/4 = 1/4.

But this makes the error stand out: we can't conclude that -1/2 = 1/2 from the equality of their squares.