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Positive reals $x, y$ satisfy $x \neq y$ and $\frac{x^2 + y^2}{xy} = k$. If replacing $x$ by $x + y$ and $y$ by $|x - y|$ leaves the value of $k$ unchanged, then $k$ equals

If $a, b, c$ are real numbers and $a^2 + b^2 + c^2 = 1$, then the set of values $ab + bc + ca$ can take is: