Linearly quadratic

Algebra Level 5

Given: x+y+z=4x+y+z=4

x2+y2+z2=6x^2+y^2+z^2=6

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

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