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Ask iit jee aieee pet cbse icse state board community Discussion Response Post to: Easy challenge
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[Post New]17 Mar 2008 15:12:34 IST
    Subject: Re:Easy challenge
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sboosy (3053)

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[tex] \\ \frac{a}{a+b+d} +\frac{b}{a+b+c}+\frac{c}{b+c+d} + \frac{d}{a+c+d} >\frac{a}{a+b+c+d} +\frac{b}{a+b+c+d}+\frac{c}{a+b+c+d} + \frac{d}{a+b+c+d} = \frac{a+b+c+d}{a+b+c+d} = 1 \\ \\ \\ \mbox{Without any loss in generality ..Consider} \ a>b>c>d \ \mbox{now} \\ \frac{a}{a+b+d} <1 \ \mbox{also} \ b+c+d < a+b+c \ \mbox{and} \ a+c+d \\ \mbox{so the last three terms} < \frac{b+c+d}{b+c+d} = 1 \\ \mbox{now adding both} \frac{a}{a+b+d} +\frac{b}{a+b+c}+\frac{c}{b+c+d} + \frac{d}{a+c+d}<1+1 = 2 \\ \\ \mbox{Thus the given expression lies between 1 and 2}
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