# 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
5 years, 3 months ago

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## Comments

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

- 5 years, 3 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.

Staff - 5 years, 3 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 ................

- 5 years, 3 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!!

- 5 years, 3 months ago

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

- 5 years, 3 months ago

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