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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, 1 month 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. C Lim · 4 years, 1 month ago

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Go to http://www.amtionline.com/ Kishan K · 4 years, 1 month ago

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@Kishan K 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, 1 month ago

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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 ago

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is it possible with just one equation? Sudipto Chowdhury · 4 years ago

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subhrodiptob@yahoo.com! i am amazed my your mathematics excellence at age of only 13!!! Subhrodipto Basu Choudhury · 4 years, 1 month ago

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cool prob which book u get this from?- mooremichael493@gmail Michael Moore · 4 years, 1 month ago

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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, 1 month ago

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What's the source of this problem? Tim Vermeulen · 4 years, 1 month ago

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@Tim Vermeulen My book. Kishan K · 4 years, 1 month ago

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@Kishan K what's the name of the book? Bhargav Das · 4 years, 1 month ago

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@Kishan K Which one is it? Does it contain more problems like this? Tim Vermeulen · 4 years, 1 month ago

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@Tim Vermeulen Yes many. Kishan K · 4 years, 1 month ago

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@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 ago

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@Kishan K may I have one? serlyayus@gmail.com Serly Zubir · 4 years ago

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@Kishan K me too ............ anshul99agr@gmail.com Anshul Agarwal · 4 years ago

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@Kishan K give it to mee too

advitiyabrijesh@gmail.com Advitiya Brijesh · 4 years, 1 month ago

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@Tim Vermeulen Give me ur email, I will send u all information of it. Kishan K · 4 years, 1 month ago

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@Kishan K pls send me too.....my mail is kislay4raj@gmail.com Kislay Raj · 4 years ago

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@Kishan K here potsunsi@yahoo.com i really interested.. Abdul Mu'min Unsi · 4 years ago

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@Kishan K chaukhanh1603@yahoo.com.vn Chau Bui · 4 years, 1 month ago

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@Kishan K Kevin, I want too, my email: leonardochandra@hotmail.com. Thanks Leonardo Chandra · 4 years, 1 month ago

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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 ago

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