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    I found this question and was wondering whether I had done this in the best way:
    (1^4+2007^4+2008^4)/(1^2+2007^2+2008^2)
    I let x be 2007 so that 2008 was x+1 and left the 1. I then simplified the expression using the usual binomial and magically got x^2+x+1 which is just
    x(x+1)+1 and therefore this simplifies to: 2007*2008+1.
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    (Original post by anshul95)
    I found this question and was wondering whether I had done this in the best way:
    (1^4+2007^4+2008^4)/(1^2+2007^2+2008^2)
    I let x be 2007 so that 2008 was x+1 and left the 1. I then simplified the expression using the usual binomial and magically got x^2+x+1 which is just
    x(x+1)+1 and therefore this simplifies to: 2007*2008+1.
    Can't say whether it's the best, but certainly a good methodology using algebra rather than slogging through numbers, and spotting that the denominator is a factor.

    As an exercise you might enjoy(?) seeing if you can generalise it, having something else there rather than "1"
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    (Original post by ghostwalker)
    Can't say whether it's the best, but certainly a good methodology using algebra rather than slogging through numbers, and spotting that the denominator is a factor.

    As an exercise you might enjoy(?) seeing if you can generalise it, having something else there rather than "1"
    That would be interesting I will investigate
 
 
 
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