Waste less time on Facebook — follow Brilliant.
×

Nice problem!

Find all integer solution to \(\frac{2}{a^{2}}+\frac{3}{b^{2}}+\frac{4}{c^{2}}=1\). Just give me a correct hint or the approach with which I must start it.Please dont give me the solution.

Note by Kishan K
4 years, 3 months ago

No vote yet
6 votes

Comments

Sort by:

Top Newest

There's a general trick here: attempt to bound one of the terms.

Let m = min(a, b, c), then \(a \ge m \implies \frac 1 {a^2} \le \frac 1 {m^2}\). Then:

\[ 1 = \frac 2 {a^2} + \frac 3 {b^2} + \frac 4 {c^2} \le 4\left( \frac 1 {a^2} + \frac 1 {b^2} + \frac 1 {c^2}\right) \le \frac {12}{m^2}\]

So \( m^2 \le 12\) and m = 2, 3. Consider each of a=2,3; b=2, 3 and c=3.

C Lim - 4 years, 3 months ago

Log in to reply

Go to http://www.amtionline.com/

Kishan K - 4 years, 3 months ago

Log in to reply

This book is not very good it is not for exam of higher level than your local exams conducted my private companies.Questions on brilliant are far far better than this.So don't bother about it anymore.Yes, If u really want to excel in mathematics get Problem Solving Strategies.Really, you will enjoy it.

Kishan K - 4 years, 3 months ago

Log in to reply

I have posted the name of the website.Many of you would be knowing it, or everyone would be.Don't go for this book it has very few questions, go for Problem Solving Strategies...Best ever book......Try to solve first few problems of it,I am not telling to solve all but few, and try to solve as many as u can....

Kishan K - 4 years, 2 months ago

Log in to reply

is it possible with just one equation?

Sudipto Chowdhury - 4 years, 3 months ago

Log in to reply

subhrodiptob@yahoo.com! i am amazed my your mathematics excellence at age of only 13!!!

Subhrodipto Basu Choudhury - 4 years, 3 months ago

Log in to reply

cool prob which book u get this from?- mooremichael493@gmail

Michael Moore - 4 years, 3 months ago

Log in to reply

Kevin, can i get your book in pdf or in word to 'playing' with your exc? my email is umaraburrohman.94@gmail.com

Umar Abdurrohman - 4 years, 3 months ago

Log in to reply

What's the source of this problem?

Tim Vermeulen - 4 years, 3 months ago

Log in to reply

My book.

Kishan K - 4 years, 3 months ago

Log in to reply

what's the name of the book?

Bhargav Das - 4 years, 3 months ago

Log in to reply

Which one is it? Does it contain more problems like this?

Tim Vermeulen - 4 years, 3 months ago

Log in to reply

@Tim Vermeulen Yes many.

Kishan K - 4 years, 3 months ago

Log in to reply

@Kishan K i am interested also.... heres my email mharfemicaroz@gmail.com

please send to me.. i have very poor math skills:(

Mharfe Micaroz - 4 years, 2 months ago

Log in to reply

@Kishan K may I have one? serlyayus@gmail.com

Serly Zubir - 4 years, 3 months ago

Log in to reply

@Kishan K me too ............ anshul99agr@gmail.com

Anshul Agarwal - 4 years, 3 months ago

Log in to reply

@Kishan K give it to mee too

advitiyabrijesh@gmail.com

Advitiya Brijesh - 4 years, 3 months ago

Log in to reply

@Tim Vermeulen Give me ur email, I will send u all information of it.

Kishan K - 4 years, 3 months ago

Log in to reply

@Kishan K pls send me too.....my mail is kislay4raj@gmail.com

Kislay Raj - 4 years, 2 months ago

Log in to reply

@Kishan K here potsunsi@yahoo.com i really interested..

Abdul Mu'min Unsi - 4 years, 2 months ago

Log in to reply

@Kishan K chaukhanh1603@yahoo.com.vn

Chau Bui - 4 years, 3 months ago

Log in to reply

@Kishan K Kevin, I want too, my email: leonardochandra@hotmail.com. Thanks

Leonardo Chandra - 4 years, 3 months ago

Log in to reply

Listen Kevin. You have got skill, talent and opportunity in front of you. Don't waste it trying to pursue some engineering degree from IIT. Instead, develop your skill and try to advance in a science stream of your choice. This is just my opinion out of my personal experience. No hard feelings against any engineering degree, engineers or any IIT.

Chinmmayya Hajare - 4 years, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...