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# Let be real numbers such that Let and be the smallest and largest possible values of respectively. Find

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Let $$x,y,z$$ be real numbers such that \begin{align*} x + y + z &= 4, \\ x^2 + y^2 + z^2 &= 6. \end{align*}
Let $$m$$ and $$M$$ be the smallest and largest possible values of $$x,$$respectively. Find $$m+M$$

Apr 27, 2019

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Let $$x,y,z$$ be real numbers such that

\begin{align*} x + y + z &= 4, \\ x^2 + y^2 + z^2 &= 6. \end{align*}
Let $$m$$ and $$M$$ be the smallest and largest possible values of $$x$$ respectively.

Find $$m+M$$

$$\begin{array}{|rcll|} \hline m+M &=& \dfrac{2}{3} + 2 \\\\ \mathbf{m+M} &\mathbf{=} & \mathbf{\dfrac{8}{3}} \\ \hline \end{array}$$

Apr 29, 2019