Linearly quadratic

Algebra Level 5

Given: \[x+y+z=4\]

\[x^2+y^2+z^2=6\]

for real numbers \(x,y\) and \(z\). If the exhaustive range of values that \(x\) can take is given by \([\alpha ,\beta]\), find \(6(\alpha +\beta)\).

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