rmo 2015-16

i am not able to solve some problems of rmo ???? but i want to crack it ??? is it be possible , can anyone suggests me the bokks ???

Note by Rudraksh Sisodia
4 years, 6 months ago

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You could tell me those problems and I may be able to help you ? See this

Rajdeep Dhingra - 4 years, 6 months ago

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http://olympiads.hbcse.tifr.res.in/uploads/crmo-2013-paper-4 here question number 3

Rudraksh Sisodia - 4 years, 6 months ago

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Method 1:

By what is also known as Titu's form of Cauchy-Schwarz we have
a2c1+b2d1+c2e1+d2a1+e2b1(a)2a520\frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge \dfrac {(\sum a)^2} {\sum a - 5} \ge 20, since it comes to (a10)20(\sum a-10)^2 \ge 0 . Equality occurs for a=b=c=d=e=2a=b=c=d=e=2


Method 2:

We know that (a2)20(a-2)^2 \ge 0 so a24(a1)a^2 \ge 4(a-1). Similarly we get a2c1+b2d1+c2e1+d2a1+e2b14(a1)c1+4(b1)d1+4(c1)e1+4(d1)a1+4(e1)b154(a1)c14(b1)d14(c1)e14(d1)a14(e1)b15=20. \frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge \frac{4(a-1)}{c-1}+\frac{4(b-1)}{d-1}+\frac{4(c-1)}{e-1}+\frac{4(d-1)}{a-1}+\frac{4(e-1)}{b-1} \\ \ge 5\sqrt[5]{\frac{4(a-1)}{c-1}\cdot \frac{4(b-1)}{d-1}\cdot \frac{4(c-1)}{e-1}\cdot \frac{4(d-1)}{a-1}\cdot \frac{4(e-1)}{b-1} }= 20 .

Rajdeep Dhingra - 4 years, 6 months ago

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@Rajdeep Dhingra heyy thnks a lot ,,, can u suggest me the books ???? are a aspirant of jee ??

Rudraksh Sisodia - 4 years, 6 months ago

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@Rajdeep Dhingra after all this question meant for which class ???

Rudraksh Sisodia - 4 years, 6 months ago

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add me also in ur hangouts ... I am also preparing for RMO! I'll give you a hand in solving the problems !!

Hrithik Nambiar - 4 years ago

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Give me your Email ID.

Rajdeep Dhingra - 4 years ago

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hrithik.nambiar2002@gmail.com

Hrithik Nambiar - 4 years ago

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thanks!

Hrithik Nambiar - 4 years ago

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Which class do ya study in ?

Rajdeep Dhingra - 4 years ago

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u can use any of the following books 1 . arthur engel 2. pre college mathematics 3 . rmo and inmo prep booklet by rajeev manocha

Rishabh Agarwal - 3 years, 11 months ago

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Can you guys help me in solving my note named :"Primes filled with primes".

Arihant Samar - 3 years, 11 months ago

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