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# Weird arithmetic Watch

1. 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.
2. (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"
3. (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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Updated: December 4, 2010
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