help me find the flaw!

[dacamogeko]

hey, my friend is challenging me to find the flaw in this proof... help me find it plz!

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

I DONT SEE A FLAW

 

[tkhunny]

Most generally, \(\displaystyle \sqrt{x^{2}}\,=\,|x|\)

\(\displaystyle \sqrt{x^{2}}\,=\,x\) ONLY if x >= 0. Take a good long look at 4 - 9/2.

It is a common thing to forget. Many teachers even argue against it. It is a very strange thing that this is so.

Burn it into your brain. \(\displaystyle \L \sqrt{x^{2}}\,=\,|x|\)

 

[dacamogeko]

ok, my friend just gave me the answer but it wasnt what u said...


They took

4 = 5

and got

-20 = -20

But whenever you multiply things you have to do it to both sides indentically:

4 * -4 = 5 * -4

4 * -5 = 5 * -5

 

[stapel]

They took 4 = 5 and got -20 = -20

Not in what you presented. Your post showed "them" starting with the "-20 = -20" and ended up with the "4 = 5". Since the starting point was valid, the problem was with a procedural step, not with the starting point (at least as the exercise was originally posted).

Eliz.

 

[tkhunny]

They took 4 = 5 and got -20 = -20

That makes no sense at all. The person who told you this does not understand this problem.

Many, many proofs, quite elegant and valid, start out with "Consider the following...". The proof then begins to do something that may seem to have absolutely nothing to do with the intended result. Sometimes it seems to be right out of the sky. It does NOT have to come from the intended result at all. It is the magic of the creative proof to show the reader how the beginning IS related to the end result, no matter how unmotivated it may have seemed at first.

It appears you would rather remember false rumors than learn the facts. Reread my answer a couple more times. This is mathematics. Let's go with the facts, not the rumors. Trust me on this. :wink: