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    (Original post by Felix Felicis)
    awesome xD
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    Isn't that just the golden ratio :angelblush:
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    Interval bisection, oh how I've missed you -.-
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    (Original post by Felix Felicis)
    How about...

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    Evaluate \sqrt{10 + \sqrt{100 + \sqrt{10 000 + \sqrt{100 000 000 + ...}}}}
    Just when I think I've got the hang of it you throw out a question which just puzzles me, hmm I'm going to get the answer even if it takes all night!
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    (Original post by Felix Felicis)
    How about...

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    Evaluate \sqrt{10 + \sqrt{100 + \sqrt{10 000 + \sqrt{100 000 000 + ...}}}}
    Where are you getting these questions from?
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    (Original post by thers)
    Where are you getting these questions from?
    The first one is pretty common: golden ratio/phi.
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    x^2+x-1=0 It doesn't factorise so ima use the formula!
     \frac{-1 + \sqrt{1+4}}{2} \therefore x=\frac{-1±+\sqrt{5}}{2} OR x=\frac{-1-\sqrt{5}}{2}

    I'm so slow :ashamed:
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    (Original post by thers)
    Where are you getting these questions from?
    Interwebz :mmm:

    (Original post by tigerz)
    x^2+x-1=0 It doesn't factorise so ima use the formula!
     \frac{-1 + \sqrt{1+4}}{2} \therefore x=\frac{-1±+\sqrt{5}}{2} OR x=\frac{-1-\sqrt{5}}{2}

    I'm so slow :ashamed:
    Indeed but the second solution is sheer lunacy, no?
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    (Original post by Felix Felicis)
    How about...

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    Evaluate \sqrt{10 + \sqrt{100 + \sqrt{10 000 + \sqrt{100 000 000 + ...}}}}
    Infinity. it's sqrt(10+10+100+1000+10000....... .)
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    (Original post by Felix Felicis)
    Interwebz :mmm:
    What site?
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    (Original post by reubenkinara)
    The first one is pretty common: golden ratio/phi.
    Yes, I thought about phi when I saw 1.618
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    (Original post by MAyman12)
    Infinity. it's sqrt(10+10+100+1000+10000....... .)
    It's not that, there's a repeating square root and it's not sqrt(10 + 10 + 100 + 1000 + 10000) it's sqrt(10 + sqrt(100 + sqrt(10000 + sqrt(100000000 + ...(i.e. the number of zeros double each time)
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    (Original post by MAyman12)
    What site?
    Not even a specific site, I just see them scattered around random maths fora when I google maths problems xD Try Math Help Forum
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    Here's a good tip on how to find out if a quadratic factorises or not: If you do b^2-4ac and it equals a square number (n^2) then it can be factorised otherwise it can't
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    (Original post by Felix Felicis)
    It's not that, there's a repeating square root and it's not sqrt(10 + 10 + 100 + 1000 + 10000) it's sqrt(10 + sqrt(100 + sqrt(10000 + sqrt(100000000 + ...(i.e. the number of zeros double each time)
    Isn't it all the same at the end, Sum to infinity? What about a hint.

    Will it end up as sqrt20 or sqrt(10+10+10+10....)
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    (Original post by Felix Felicis)
    ...
    Could you give me a little pointer in this question as what I've been doing is x = sqrt(10+x^2) which is complete rubbish as 10 = 0 from it.
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    (Original post by MAyman12)
    Isn't it all the same at the end, Sum to infinity? What about a hint.
    Yes, it is a sum to infinity but it converges

    Try testing for small powers of 10
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    (Original post by MathsNerd1)
    Could you give me a little pointer in this question as what I've been doing is x = sqrt(10+x^2) which is complete rubbish as 10 = 0 from it.
    Try testing for small powers of 10 and see how the expression simplifies
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    (Original post by Felix Felicis)
    How about...

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    Evaluate \sqrt{10 + \sqrt{100 + \sqrt{10 000 + \sqrt{100 000 000 + ...}}}}
    Pf, at least make the result pretty Felix:

    \sqrt{\dfrac{1}{\phi^2}+ \sqrt{\dfrac{1}{\phi^4}+ \sqrt{\dfrac{1}{\phi^8}+\cdots}}  }

    ... or something
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    (Original post by Felix Felicis)

    Indeed but the second solution is sheer lunacy, no?
    OH yeah, is it because all the ones are positive, so x can't be negative? +/+=+ lols

    Also am I heading in the right direction in saying:

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    x=\sqrt{10+\sqrt{10^2+\sqrt{10^4  +\sqrt{10^8}}}} then simplifying further by doing some cancelling?


    BRB, gonna take my dog to the park lols
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    (Original post by Felix Felicis)
    Yes, it is a sum to infinity but it converges

    Try testing for small powers of 10
    (1+sqrt(41))/2
 
 
 
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