# 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
6 years, 4 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

• bulleted
• list

1. numbered
2. list

1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

- 6 years, 4 months ago

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

- 6 years, 4 months ago

- 6 years, 4 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 $\frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge \frac{4(a-1)}{c-1}+\frac{4(b-1)}{d-1}+\frac{4(c-1)}{e-1}+\frac{4(d-1)}{a-1}+\frac{4(e-1)}{b-1} \\ \ge 5\sqrt[5]{\frac{4(a-1)}{c-1}\cdot \frac{4(b-1)}{d-1}\cdot \frac{4(c-1)}{e-1}\cdot \frac{4(d-1)}{a-1}\cdot \frac{4(e-1)}{b-1} }= 20 .$

- 6 years, 4 months ago

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

- 6 years, 4 months ago

after all this question meant for which class ???

- 6 years, 4 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, 10 months ago

- 5 years, 10 months ago

hrithik.nambiar2002@gmail.com

- 5 years, 10 months ago

thanks!

- 5 years, 10 months ago

Which class do ya study in ?

- 5 years, 10 months 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

- 5 years, 9 months ago

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

- 5 years, 9 months ago