If $x,y,z\in [0,\infty )$ such that $x+y+z=3$ prove that $27\leq \left( x^{2}+2\right) \left( y^{2}+2\right) \left( z^{2}+2\right) \leq 44$. I tried to use the relation $x^{2}+2\leq x^{2}+3x+2,x\geq 0$, but without success.
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1this was solved already in this forum – Dr. Sonnhard Graubner Jan 20 '18 at 19:28
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See here: https://math.stackexchange.com/questions/2584515 – Michael Rozenberg Jan 20 '18 at 19:43