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 Question from Nitin, a teacher: If x+y+z=1 then x^2 +y^2+z^2 = ? ?

This question has no single answer.

The graph of $x+y+x = 1$ is a plane passing through $(1,0,0), (0,1,0)$, and $(0,0,1).$ It has infinitely many points in it.

$x^2 + y^2 + z^2$ is the square of the distance from the origin to a point. For points in this plane it can take any value greater than or equal to 1/3 (achieved at (1/3,1/3,1/3).)

Good Hunting!
RD