Non-Homogenous Inequality

Algebra Level 4

x+y+z+xy+yz+xz\large x+y+z+xy+yz+xz

Over all real x,yx,y and zz satisfying x2+y2+z2=1x^2+y^2+z^2 = 1, find the minimum value of the above expression.


Inspiration.

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