let-x-y-z-0-and-x-2-y-2-z-2-12-find-the-min-value-of-S-x-y-z-xyz-1-xy-yz-zx-

Question Number 153381 by mathdanisur last updated on 06/Sep/21

let x; y; z ⩾ 0 and x^{2} + y^{2} + z^{2} = 12

find the \min value of

S = x + y + z + xyz + \frac{1}{xy + yz + zx}

Commented by mr W last updated on 06/Sep/21

S_{m i n} = 3 \times 2 + 2^{3} + \frac{1}{3 \times 2^{2}} = \frac{169}{12}

Commented by mathdanisur last updated on 07/Sep/21

No ser = \frac{9}{2}