Find \(ab + bc + ca\) given that:

\(a^{2} + ab + b^{2} = 2\)

\(b^{2} + bc + c^{2} = 1\)

\(c^{2} + ca + a^{2} = 3\)

Giveb that a, b, and c are positive numbers.

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## Comments

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TopNewestComment deleted Mar 06, 2017

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@Aneesh Kundu I know its a very late reply , still .. Isn't your Eq 5 wrong?

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You're right.

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Christian Daang has posted the same problem recently.

Here

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Yah sir, after a year and a half, I figure it out how this can be solve. :)

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By the way , you post some really interesting questions ...I love them.

Even you can try my sets out

My Problems and THRILLER

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Its absolutely brilliant that you have devised your own method...:) :) :)

Please don't call me sir , I am your fellow BRILLIANTIAN and a FRIEND.

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~ Do you think there are other ways to solve this except for the geometric method?

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Is the question correct? There don't exist positive \(a,b,c \) for which these equations are true.

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Yes sir, there is. :)

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