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
5 years, 2 months ago

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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.

- 5 years, 2 months ago

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

- 5 years, 2 months ago

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.

- 5 years, 2 months ago

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....

- 5 years, 2 months ago

is it possible with just one equation?

- 5 years, 2 months ago

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

- 5 years, 2 months ago

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

- 5 years, 2 months ago

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

- 5 years, 2 months ago

What's the source of this problem?

- 5 years, 2 months ago

My book.

- 5 years, 2 months ago

what's the name of the book?

- 5 years, 2 months ago

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

- 5 years, 2 months ago

Yes many.

- 5 years, 2 months ago

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

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

- 5 years, 2 months ago

may I have one? serlyayus@gmail.com

- 5 years, 2 months ago

me too ............ anshul99agr@gmail.com

- 5 years, 2 months ago

give it to mee too

- 5 years, 2 months ago

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

- 5 years, 2 months ago

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

- 5 years, 2 months ago

here potsunsi@yahoo.com i really interested..

- 5 years, 2 months ago

chaukhanh1603@yahoo.com.vn

- 5 years, 2 months ago

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

- 5 years, 2 months ago

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.

- 5 years, 2 months ago