Phaze's Brainteaser of the Day #1 01-16-2013, 05:12 AM
#1
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:
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.
Which step is wrong, and why?
Brainteaser #2
What step is the error located in?
Correct Responses:
Final Note:
Always feel free to PM me suggestions to puzzles for me to derive/look up/modify!
A bit about why I'm doing this:
Spoiler:
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 = 1Which 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!
![[+]](https://sinister.ly/images/modern/collapse_collapsed.png)
![[Image: 57sQsY2.png]](http://i.imgur.com/57sQsY2.png)
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!