Annoying algebra in today's pre-RMO !

Hello !

Today was my Pre-RMO . I was stuck in the following question please help .

If

sin1x+sin1y+sin1z=3π2 \sin^{-1} x + \sin^{-1} y + \sin^{-1} z = \dfrac{3 \pi}{2}

Then find the value of :

x9+y9+z9+1x9y9z9 x^9 + y^9 + z^9 + \dfrac{1}{x^9y^9z^9}

Well , I had got the following result from this : ( Might be wrong )

x+y+z=1 x + y + z = -1

but I couldn't manage to do it any further . Please help .

Note by Priyansh Sangule
6 years ago

No vote yet
11 votes

  Easy Math Editor

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.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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

[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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

The range of sin1\sin^{-1} is [12π,12π][-\tfrac12\pi,\tfrac12\pi]. Since sin1x+sin1y+sin1z=32π\sin^{-1}x+\sin^{-1}y+\sin^{-1}z = \tfrac32\pi, we know the values of sin1x,sin1y,sin1z\sin^{-1}x,\sin^{-1}y,\sin^{-1}z straight away (what three numbers between a-a and aa add to 3a3a?). Thus we know x,y,zx,y,z.

Mark Hennings - 6 years ago

Log in to reply

Thank You !

Priyansh Sangule - 6 years ago

Log in to reply

Very simple one! As, sin1x[π2,π2]\sin^{-1} x \to [\frac{- \pi}{2}, \frac{\pi}{2}]

So, it leads us to the conclusion that x=1,y=1,z=1x=1, y=1, z=1

Then, required value becomes 4\boxed{4}

Advitiya Brijesh - 6 years ago

Log in to reply

i thought same . quite easy.

umang garg - 5 years, 10 months ago

Log in to reply

max value of the following equation is 3pi/2 and hence each angle should be pi/2. if angle is pi/2 then x=y=z=1 then 1 + 1 + 1 + 1 = 4. That's it

Vaibhav Reddy - 6 years ago

Log in to reply

What is Pre-RMO? Is the full paper available somewhere?

Thanks!

Pranav Arora - 6 years ago

Log in to reply

Well this time , the government has allowed every state to set their own papers for pre-RMO . That is the qualification stage for RMO level 1 .

Priyansh Sangule - 6 years ago

Log in to reply

In Telangana region,there is no pre-RMO....lucky for me I can directly write RMO paper without qualifying.... BTW....The RMO exam is not so easy as pre-RMO....I was dying to solve some of them...

Vaibhav Reddy - 6 years ago

Log in to reply

In Mumbai region there is Pre-RMO, as the no. of students taking part was much more. While the other regions in the country have RMO directly (including other-than-Mumbai Maharashtra part. We are going to give it on 1st December. Let's discuss some good problems thereafter...!!!

Yash Jakhotiya - 6 years ago

Log in to reply

Promo paper

dhanesh shah - 2 years, 2 months ago

Log in to reply

Priansh, can I get the copy of your PRMO paper??

CCD Pandhare - 5 years, 12 months ago

Log in to reply

Well they didn't allow us to take it back home :/

Priyansh Sangule - 5 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...