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Apr 8, 2018 at 20:54 comment added Malkoun Well, I know it is true from another point of view... It would take some time to explain. Email me if you want. I will reply tomorrow.
Apr 8, 2018 at 20:53 comment added Iosif Pinelis I think it is helpful, when one poses a conjecture, to also indicate reasons why the conjecture seems plausible.
Apr 8, 2018 at 20:43 comment added Malkoun I checked my equations. Sorry, I had a mistake in them. I will edit my post...
Apr 8, 2018 at 20:26 comment added Iosif Pinelis I have added a counterexample satisfying also the additional condition that the points $\mathbf x_i=(x_i,y_i,z_i)$ be nonzero.
Apr 8, 2018 at 20:23 history edited Iosif Pinelis CC BY-SA 3.0
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Apr 8, 2018 at 20:15 comment added Malkoun I will also rederive the equations tomorrow to double check.
Apr 8, 2018 at 20:13 comment added Malkoun oops I forgot to mention the $3$ points are in $\mathbb{R}^3 \setminus 0$. None of them can be at the origin.
Apr 8, 2018 at 19:38 comment added Malkoun ok Thank you. It means I made a calculation mistake. I will correct my post tomorrow. Thank you though!
Apr 8, 2018 at 19:36 history answered Iosif Pinelis CC BY-SA 3.0