Posted by shish on Sunday, June 8, 2014 at 2:25pm.
the no. of real roots of eqn (x1)POWER 2 + (X2) POWER 2 +(X3) POWER 2= 0 IS:

math  Steve, Sunday, June 8, 2014 at 7:21pm
lose all the nonsense text. You have
(x1)^2 + (x2)^2 + (x3)^2 = 0
Now, you know that (x1)^2 is a parabola, which is tangent to the xaxis at x=1, because of the double root.
Similarly, the other two terms are never negative. So, since we are adding up three positive values for each x, the graph will never cross the xaxis, meaning there are no real roots.
Or, try expanding things to get
3x^212x+14=0
Since the discriminant is negative, there are no real roots.