# 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
7 years 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.

- 7 years ago

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

- 7 years 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.

- 7 years ago

What's the source of this problem?

- 7 years ago

My book.

- 7 years ago

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

- 7 years ago

Yes many.

- 7 years ago

give it to mee too

- 7 years ago

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

- 7 years ago

may I have one? serlyayus@gmail.com

- 7 years ago

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

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

- 7 years ago

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

- 7 years ago

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

- 7 years ago

chaukhanh1603@yahoo.com.vn

- 7 years ago

here potsunsi@yahoo.com i really interested..

- 7 years ago

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

- 7 years ago

what's the name of the book?

- 7 years ago

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

- 7 years ago

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

- 7 years ago

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

is it possible with just one equation?

- 7 years 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....

- 7 years 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.

- 7 years ago