 Posers and Puzzles

1. 27 Aug '03 19:58
I guess one could probably find this somewhere on the internet; but, can anyone tell me why this is incorrect:

-20=-20
16-36=-20
25-45=-20
16-36=25-45
16-36+(81/4)=25-45+(81/4)
(4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
4-(9/2)=5-(9/2)
4=5
1=2 (subtracting 3 from each side)
2. 27 Aug '03 20:14
Originally posted by Cheshire Cat
I guess one could probably find this somewhere on the internet; but, can anyone tell me why this is incorrect:

-20=-20
16-36=-20
25-45=-20
16-36=25-45
16-36+(81/4)=25-45+(81/4)
(4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
4-(9/2)=5-(9/2)
4=5
1=2 (subtracting 3 from each side)
You are taking the negative root of the expression on the left and the positive root of the expression on the right.

Another example:
(-2)^2 = 4
(2)^2 = 4
(-2)^2 = (2)^2
-2 = 2
3. 27 Aug '03 20:171 edit
Originally posted by richjohnson
You are taking the negative root of the expression on the left and the positive root of the expression on the right.

Another example:
(-2)^2 = 4
(2)^2 = 4
(-2)^2 = (2)^2
-2 = 2
I see. Does that mean that the correct answer would be something like 2i=2?
4. 27 Aug '03 20:371 edit
No.

(-2)^2 = 2^2=4

All this is an indication of is the fact that every positive real number has two real square roots.

(2i)^2 = -4
5. 27 Aug '03 20:45
Originally posted by royalchicken
No.

(-2)^2 = 2^2=4

All this is an indication of is the fact that every positive real number has two real square roots.

(2i)^2 = -4
Right....does that also apply to the first equation?
6. 27 Aug '03 21:01
(4-(9/2))^2=(-0.5)^2

(5-(9/2))^2=(0.5)^2

As richjohnson said, you can't make the negative and positive roots equivalent.
7. 27 Aug '03 21:14
Originally posted by royalchicken
(4-(9/2))^2=(-0.5)^2

(5-(9/2))^2=(0.5)^2

As richjohnson said, you can't make the negative and positive roots equivalent.

x=.999999999....repeating 9s
10x=9.999999....repeating 9s

Using systems I think:

~~~~10x=9.999....~~~
~~~~~-x=.9999....~~~
---------------------------

~~~~~9x=9~~~~~~~~

x=1
x=.99999....

1=.999999......

Hope that is understandable.
8. 27 Aug '03 21:16
Originally posted by Cheshire Cat

x=.999999999....repeating 9s
10x=9.999999....repeating 9s

Using systems I think:

~~~~10x=9.999....~~~
~~~~~-x=.9999....~~~
---------------------------

~~~~~9x=9~~~~~~~~

x=1
x=.99999....

1=.999999......

Hope that is understandable.
That's fine, since 1 = 0.9 rec. There's another thread on this in this forum. Good job, though.
9. 27 Aug '03 21:21
Originally posted by royalchicken
That's fine, since 1 = 0.9 rec. There's another thread on this in this forum. Good job, though.
Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
10. 27 Aug '03 21:27
Originally posted by Cheshire Cat
Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
They are actually the same number (rec = &quot;recurring&quot😉.

Incidentally, the series S=(1/2 + 1/4 + 1/8 + 1/16 + ...) is also equal to one.

Why?

2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...)

2S-S=1
11. 27 Aug '03 21:30
Originally posted by Cheshire Cat
Why does this work though? Obviously they are two different numbers. And what is your abbreviation rec.?
Yeah, sorry. 09. rec is shorthand for 0.999999999999999999...........
12. 27 Aug '03 21:35
Originally posted by richjohnson
They are actually the same number (rec = "recurring"😉.

Incidentally, the series S=(1/2 + 1/4 + 1/8 + 1/16 + ...) is also equal to one.

Why?

2S=(1 + 1/2 + 1/4 + 1/8 + 1/16 + ...)

2S-S=1
That's all well and good, but the question is why do they work.
13. 28 Aug '03 01:161 edit
-20=-20
16-36=-20
25-45=-20
16-36=25-45
16-36+(81/4)=25-45+(81/4)
(4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
4-(9/2)=5-(9/2)
4=5
1=2 (subtracting 3 from each side)

the first problem works due, as RichJohnson said, because all positive real numbers have two roots both the negative and the positive. Therefore, if you take 2^2 and -2^2 you will get 4 for both. The reason this works is because the eqaution, although, mathematically correct is not balanced correctly. (Or, atleast thats what my maths teacher would say as I messed up a question, in a paper, because I did just this and got the wrong answer🙂)

x=.999999999....repeating 9s
10x=9.999999....repeating 9s

Using systems I think:

~~~~10x=9.999....~~~
~~~~~-x=.9999....~~~
---------------------------

~~~~~9x=9~~~~~~~~

x=1
x=.99999....

1=.999999......

Hope that is understandable.

the second was explained to me but I can't for the life of me remember. I'll ask some people and see if they can tell me.
14. 28 Aug '03 01:31
Originally posted by jimmi t
[b]-20=-20
16-36=-20
25-45=-20
16-36=25-45
16-36+(81/4)=25-45+(81/4)
(4-(9/2))^2=(5-(9/2))^2 (factoring, I think)
4-(9/2)=5-(9/2)
4=5
1=2 (subtracting 3 from each side)

the first problem works due, as RichJohnson said, because all positive real numbers have two roots both the negative and the positive. Therefore, if you take 2^2 and -2 ...[text shortened]... me but I can't for the life of me remember. I'll ask some people and see if they can tell me.[/b]
Cool, thanks.
15. 28 Aug '03 09:19
One canalso think asfollows

1/9 = 0.11111111111111111111...
2/9 = 0.22222222222222222222...
3/9 = 0.333333333333333333...
:
:
9/9 = 0.999999999999999999...