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## #1 2006-02-06 10:48:11

NoSash
Member
Registered: 2006-02-06
Posts: 7

### Four Equals Five

1)                           16 - 36 = 25 - 45
2)                16 - 36 + 81/4 = 25 - 45 + 81/4
3) 4^2 - 2x4x9/2 + (9/2)^2 = 5^2 - 2x5x9/2 + (9/2)^2
4)                     (4 - 9/2)^2 = (5 - 9/2)^2
5)                           4 - 9/2 = 5 - 9/2
6)                                   4 = 5

What went wrong?

I'm pretty sure the error is from step 3 to 4 but I don't know what the heck they are trying to do.

Last edited by NoSash (2006-02-06 10:57:55)

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## #2 2006-02-06 10:58:00

Member
Registered: 2005-11-28
Posts: 97

### Re: Four Equals Five

when you take the square root, you need the ± which gives you a few different combinations...this "proof" just uses one combination that does not work.

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
-Bertrand Russell

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## #3 2006-02-06 18:57:01

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Four Equals Five

e.a.
4)                     (4 - 9/2)^2 = (5 - 9/2)^2
5)                            |4-9/2|=|5-9/2|
6)                              |-0.5|=|+0.5|
which is OK.

Last edited by krassi_holmz (2006-02-06 18:57:47)

IPBLE:  Increasing Performance By Lowering Expectations.

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## #4 2006-02-06 20:47:56

kempos
Member
Registered: 2006-01-07
Posts: 77

### Re: Four Equals Five

step 5. there you should have absolute value.

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## #5 2006-02-06 21:00:30

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Four Equals Five

Yep.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #6 2006-02-07 04:37:19

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Four Equals Five

All of the above is correct. They've hidden it with lots of unnecessary complications, but what they're basically doing is saying that as x² = (-x)², then x = -x, even though it doesn't.

Why did the vector cross the road?
It wanted to be normal.

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## #7 2006-02-07 04:51:39

NoSash
Member
Registered: 2006-02-06
Posts: 7

### Re: Four Equals Five

yeah it all makes sense, thanks guys

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## #8 2006-02-13 11:52:50

NoSash
Member
Registered: 2006-02-06
Posts: 7

### Re: Four Equals Five

Hey guys, apparently it's incorrect to put the absolute value signs, can anybody confirm this? Or support it? I know it works out mathematically but I was told it's still wrong.

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