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Mmmm......I should know better than to deal with people who read the fine print and take everything literally......there's a term for those folks....."future lawyers"

The question mentions interations so I suppose this is the correct interpretation 

BUT

where does it say in the question that       $$x_n=f(x_{(n-1)})$$

all I see is that   $$f(x)=x^2-i$$

I can certainly see that  $$x_0=1+i$$

I am completely unfamiliar with this wording (notation).

You lost me at the word,  "dissociates"......The rest???.....I'll take your word for it......

(I'll give you 3 points even if you made up a good story.....at least it looks impressive)

Actually......any number of things might "fit" into the box....  ³√27, ±⁴√81, the integer part of "pi".......etc.

Melody....we're just putting x₀ = 1 + i into  x² + c  and evaluating that, first...

So we have

(1 + i)² + (-i)  =   (1 + 2i - i²) - i     = ( 1 + 2i - 1) - i  = i  = x₁

Then, we're putting this result back into x² + c to get x₂ =

(i)² - i = -1 - i  .......then we put this back into x² + c  to get x₃

So on and so forth......and as Alan notes.....it sets up a repeating "2 cycle" pattern

$$(2)^{0.2} = \sqrt[5]{2}$$

This means, what multiplied by itself 5 times =2

that is find $$a$$ if    $$a\times a\times a\times a\times a=2$$

This is too difficult to do by hand.  You  need to use a calculator.  

Even then it will be an approximation because this will be an irrational number.  The digits will go on for ever.

That is a very good point.  You could too  

You could also write -3 in the box.

two numbers have LCM of 20 and HCF of 2 what are they

Lets think about this

Since 2 is a common factor the numbers have to both be even and 

since 20 is a multiple of both, they both have to go into 20

which even number go into 20

2,4,10,20  that is it.  

20 and 2 work,

10 and 4 work

I don't think any other pair works for this.

@@ End of Day Wrap           Sat 6/12/14         Sydney,   Australia          Time 6:25 pm         ♬

Good evening,  

I am sorry  that sometimes I accidently leave people off the credit list.  If this has happened to you then I appologise.  Generally speaking I only include members who seriously attempt to answer a question.  If you were just playing then you may not be included.  

Today our answerers included.  CPhill, Mathematician, Alan, Heureka, saseflower, shaniab29544, Happy7, MamaLlama and Sorasyn.  Thank you all.

I also miss DragonSlayer554 and Zegroes.  I wish they would return.  There are others that have passed this way that I also miss very much.  The others that come most to mind are Rom, Professor Lopez and Puzzled.  Kitty and the troll are the only other ones who are likely to remember the later two.  It is easy to lose track of people in life and in a forum environment like this one it is much easier again.  I get sad when I think about it.     Still, on the plus side whe have few wonderful new people who have filled the void (to some extent anyway).  I guess it is the natural cylce of regeneration.  

Anyway, here are some interest posts:

1) A little riddle.  There were a few of these.    Thanks Happy and anon  

Sun 7/12/14

1) This one is great - calc the 5th root of 2 with a very simple calculator - Thanks anon :)

(Suitable for all high school children - at a push anyway)

I do not know if it is correct but I will give you 3 points for your efforts  

Anonymous got this one correct Chris - You got it wrong.      Nananana    

Thanks Heureka :)

$$\\x^4=1.15925926\times 10^{-12}\\\\
(x^4)^{1/4}=(1.15925926\times 10^{-12})^{1/4}\\\\
x=1.15925926^{0.25}\times 10^{-12*0.25}\\\\
x=1.15925926^{0.25}\times 10^{-3}\\\\$$

You can finish it on the calc on the home page.

$$days=-10.08\div -1.26$$

$$\\4x^2-24x+32=0\\
$first simplify by dividing both sides by 4$\\
x^2-6x+8=0\\
$You need 2 numbers that mult to +8 and add to -6$\\
$ These numbers will be -4 and -2$\\
(x-4)(x-2)=0\\
x=4 \;or \;x=2$$

I don't understand this question.

No it isn't brittany

a negative number plus a negative number has to be a negative number

eg

You can think of neg numbers as being cold numbers

It is cold (less than 0)   you add more cold  the temperature goes down even more

-6                                   +           -8               = -14

The number is too huge to expess in any normal way.  BUT it is not infinity .

ex.

6% of 7% = 0.06*0.07 = 0042 = 0.43%

$$i=0.015/3,\quad n=6*3=18\\

FV=P(1+i)^n$$

C=1000

i=0.07

n= 5

Can you take it from here?

I don't understand Alan