# 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
5 years, 6 months ago

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- 5 years, 6 months ago

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

- 5 years, 6 months ago

- 5 years, 6 months ago

Method 1:

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

Method 2:

We know that $(a-2)^2 \ge 0$ so $a^2 \ge 4(a-1)$. Similarly we get $\frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge \frac{4(a-1)}{c-1}+\frac{4(b-1)}{d-1}+\frac{4(c-1)}{e-1}+\frac{4(d-1)}{a-1}+\frac{4(e-1)}{b-1} \\ \ge 5\sqrt[5]{\frac{4(a-1)}{c-1}\cdot \frac{4(b-1)}{d-1}\cdot \frac{4(c-1)}{e-1}\cdot \frac{4(d-1)}{a-1}\cdot \frac{4(e-1)}{b-1} }= 20 .$

- 5 years, 6 months ago

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

- 5 years, 6 months ago

after all this question meant for which class ???

- 5 years, 6 months ago

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

- 5 years ago

- 5 years ago

hrithik.nambiar2002@gmail.com

- 5 years ago

thanks!

- 5 years ago

Which class do ya study in ?

- 5 years ago

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

- 4 years, 10 months ago

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

- 4 years, 11 months ago