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

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 \(m+M\)

see: https://doubtnut.com/question-answer/if-x-y-z-are-real-such-that-x-y-z4x2-y2-z2-6-then-x-in-1-11-2-0-2-3-23-42-32-2232900

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