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Given: x+y+z=4x+y+z=4x+y+z=4
x2+y2+z2=6x^2+y^2+z^2=6x2+y2+z2=6
for real numbers x,yx,yx,y and zzz. If the exhaustive range of values that xxx can take is given by [α,β][\alpha ,\beta][α,β], find 6(α+β)6(\alpha +\beta)6(α+β).
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