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The key to simplifying monstrous equations

Main post link -> https://brilliant.org/i/qT4TKa/

This problems leads to a huge equation,

4(a+b+c) +2(ab+bc+ac)+abc=1741

Can I get some help from you guys solving it.. I got lazy and solved it with Python, but that surely isn't the best way..

Note by Aasif Khan
4 years, 7 months ago

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apply Vieta's formula and form an equation whose roots are a,b and c.......

Kiran Patel - 4 years, 7 months ago

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A problem can have more than 1 solution. There is a very pretty way of looking at it. Think about how to use the condition that \(a, b, c\) are integers.

Note that your \(a, b, c\) do not correspond to the \(a, b, c\) in the question.

Calvin Lin Staff - 4 years, 7 months ago

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then what to do cALVIN, can you give a hint,so that i CAN PROCEED...........and please check whether I am correct or not ................

Kiran Patel - 4 years, 7 months ago

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I know I might sound a bit, naive, but you're actually saying that solving this equation is pretty easy, all I need to do is find the right way to look at it!!

Aasif Khan - 4 years, 7 months ago

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Hint: see if you can factorize \(4(p+q+r)+2(pq+qr+rp)+pqr+8\). ;)

Arkan Megraoui - 4 years, 7 months ago

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