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.

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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@Aneesh Kundu I know its a very late reply , still .. Isn't your Eq 5 wrong? – Ankit Kumar Jain · 4 months, 3 weeks ago

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– Aneesh Kundu · 4 months, 2 weeks ago

You're right.Log in to reply

Christian Daang has posted the same problem recently.

Here – Ankit Kumar Jain · 4 months, 2 weeks ago

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– Christian Daang · 4 months, 2 weeks ago

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

Even you can try my sets out

My Problems and THRILLER – Ankit Kumar Jain · 4 months, 2 weeks ago

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Please don't call me sir , I am your fellow BRILLIANTIAN and a FRIEND. – Ankit Kumar Jain · 4 months, 2 weeks ago

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~ Do you think there are other ways to solve this except for the geometric method? – Christian Daang · 4 months, 2 weeks ago

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– Ankit Kumar Jain · 4 months, 2 weeks ago

At present , I can't think of any other way.Log in to reply

Is the question correct? There don't exist positive \(a,b,c \) for which these equations are true. – Siddhartha Srivastava · 1 year, 10 months ago

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– Christian Daang · 1 year, 10 months ago

Yes sir, there is. :)Log in to reply