# Help Me!

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.

Note by Christian Daang
2 years, 6 months ago

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Comment deleted Mar 06, 2017

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

- 1 year, 1 month ago

You're right.

- 1 year, 1 month ago

Christian Daang has posted the same problem recently.

- 1 year, 1 month ago

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

- 1 year, 1 month ago

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

Even you can try my sets out

- 1 year, 1 month ago

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

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

- 1 year, 1 month ago

I saw someone who figure it out how this can be solve. :) I just somewhat get it. XD And somewhat make it more elaborative.

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

- 1 year, 1 month ago

At present , I can't think of any other way.

- 1 year, 1 month ago

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

- 2 years, 6 months ago

Yes sir, there is. :)

- 2 years, 6 months ago