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#1 Posted 10:35am 10-03-10 quite a good oneWrite 271 as the sum of positive real numbers so as to maximize their product [hide]more of calculus than algebra[4][/hide] |
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#2 Posted 11:17am 10-03-10 Re: quite a good onea1+a2+a3+....+an = 271 we need to maximise a1*a2*a3*....*an from AM-GM (271)/n ≥ (product)[p]1/n[/p] => product ≤ (271/n)[p]n[/p] consider f(x) = (271/x)[p]x[/p] lnf(x) = x*ln(271) - x*lnx f'(x)/f(x) = ln(271) - 1 - lnx = 0 => lnx = ln(271/e) => x = 271/e = 99.69 so 271 = e*(271/e) each part is 271/e
IIT has walked to me ... off to IIT K |
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#3 Posted 11:19am 10-03-10 Re: quite a good onecorrect :) |
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