# 1 Equation 3 variables!

Algebra Level 4

$\left ( 1-x \right )^{2}+\left ( x-y \right )^{2}+\left ( y-z \right )^{2}+z^{2}=\frac{1}{4}$ Find all real numbers $$x, y, z$$ such that this equation is satisfied. If there exists only one ordered triplet $$(x,y,z)$$ that satisfies the equation. Then submit your answer as $\sqrt{\frac{x}{3}}+6y+\sqrt{z}.$

Bonus: Prove that there exists only one ordered triplet of $$(x,y,z)$$.

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