Define the equality.
Add a constant (16) to each side.
Express the equality as a binomial.
Take the square root of each side.
Add a constant (4) to each side.
This is somewhat different from the Proof that 4 = 3 and the Proof that -1 is a positive number.
Found at Futility Closet, which is where the others came from; it's a wonderful resource for those interested in mathematical playfulness and humor.
You can't just "take the square root of each side". Taking the square root yields the absolute value. This leaves you with:
ReplyDelete(3-4)^2=(5-4)^2
|3-4|=|5-4|
|-1|=|1|
1=1
Well, I suppose the reply to that would be to refer you to the other one which explains that -1 is actually a positive number...
ReplyDelete:.)
Q.E.D.!
ReplyDeleteit doesn't work like that...when you take the square of both sides, there are actually four possible solutions that need to ALL be evaluate. this is THE KEY STEP in any simplification involving square-rooting of both sides of an equation.
ReplyDelete-(3-4) = -(5-4)
-(3-4) = +(5-4)
+(3-4) = -(5-4)
+(3-4) = +(5-4)
only the solutions that leave you with 1=1 or -1=-1 are right. the other ones are crossed out.
But it also has a possibility does not exist, an equation, root, if you use eg
ReplyDelete(3 +4) ² = (5 +4) ²
because if you cut them you root ends with 3 = 5.
Very good.
ReplyDelete