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Phaze's Brainteaser of the Day #1 - Printable Version

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Phaze's Brainteaser of the Day #1 - Soul - 01-16-2013

Hey guys, I want to start up a mini-thread-series where I just post some interesting brainteasers about science, math, technology, etc.

A bit about why I'm doing this:
Spoiler:
I feel that having a bit of brain exercise every day can lead to a healthy lifestyle. I'm not forcing you to read this or attempt the brainteaser, but it's definitely some good brainfood to munch on over breakfast or lunch. Feel free to post solutions, but please make sure to explain your reasoning. After all, it's for your own good!

The Brainteaser:
This is one I wrote up myself, although I'll admit I derived it from another mathematical farce.

Anyways, here's my process of work.
Code:
a = b    //Set a equal to b    
a² = ab    //Multiply both sides by a.
a² - b² = ab - b²    //Subtract "b²" from both sides.
(a + b)(a - b) = b(a - b)    //Use FOIL and factor both sides.
(a + b) = b    //Divide both sides by (a - b).
2b = b  //Since a = b, substitute b for a to get 2b = b.
2 = 1

Which step is wrong, and why?

Brainteaser #2
Code:
-1/1 = 1/(-1)  
Sqrt(-1/1) = Sqrt(1/-1)  //Take the square root of both sides
Sqrt(-1)/Sqrt(1) = Sqrt(1)/Sqrt(-1)   //Break up the square roots
Therefore, i/2 = 1/(2i)
i/2 + 3/(2i) = i/(2i) + 3/(2i)    //Add 3/(2i) to both sides
i*[i/2 + 3/(2i)] = i*[1/(2i) + 3/(2i)]   //Multiply both sides by i
(i^2)/2 +3/2 = 1/2 + 3/2    //Simplify the previous step
-1/2 + 3/2 = 1/2 + 3/2  //Simplify again
1 = 2    //Fin.

What step is the error located in?

Correct Responses:
Spoiler:

Final Note:
Always feel free to PM me suggestions to puzzles for me to derive/look up/modify!

RE: Phaze's Brainteaser of the Day #1 - Falcon - 01-16-2013

Looked at it....Looked at it again...Thought for a bit...Gave up.

LOL.

Good luck everyone Smile

RE: Phaze's Brainteaser of the Day #1 - Soul - 01-16-2013

(01-16-2013, 05:17 AM)Falcon Wrote: Looked at it....Looked at it again...Thought for a bit...Gave up.

LOL.

Good luck everyone Smile

It's a bit hard, takes a long time to figure out Tongue I highly encourage that you muse over it when you're bored. Helps a lot with speeding up your brain and picking up small details!

RE: Phaze's Brainteaser of the Day #1 - Falcon - 01-16-2013

(01-16-2013, 05:19 AM)Phaze Wrote:
(01-16-2013, 05:17 AM)Falcon Wrote: Looked at it....Looked at it again...Thought for a bit...Gave up.

LOL.

Good luck everyone Smile

It's a bit hard, takes a long time to figure out Tongue I highly encourage that you muse over it when you're bored. Helps a lot with speeding up your brain and picking up small details!

I'm going to try again in a few. Have to make some of the groups sub forums.