# 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
3 years, 9 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. 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 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> 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:

- 3 years, 9 months ago

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

- 3 years, 9 months ago

- 3 years, 9 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 $$\frac{a^2}{c-1}+\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1} \ge \frac{4(a-1)}{c-1}+\frac{4(b-1)}{d-1}+\frac{4(c-1)}{e-1}+\frac{4(d-1)}{a-1}+\frac{4(e-1)}{b-1} \\ \ge 5\sqrt[5]{\frac{4(a-1)}{c-1}\cdot \frac{4(b-1)}{d-1}\cdot \frac{4(c-1)}{e-1}\cdot \frac{4(d-1)}{a-1}\cdot \frac{4(e-1)}{b-1} }= 20 .$$

- 3 years, 9 months ago

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

- 3 years, 9 months ago

after all this question meant for which class ???

- 3 years, 9 months ago

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

- 3 years, 3 months ago

- 3 years, 3 months ago

hrithik.nambiar2002@gmail.com

- 3 years, 3 months ago

thanks!

- 3 years, 3 months ago

Which class do ya study in ?

- 3 years, 3 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

- 3 years, 2 months ago

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

- 3 years, 2 months ago