<s>[INST] If $a,b,c>0$ and $abc=1\;,$ Then minimum value of Expression. 
If $a,b,c>0$ and $abc=1\;,$ Then minimum value of $$\frac{a^2}{a^2+2}+\frac{b^2}{b^2+2}+\frac{c^2}{c^2+2}$$

$\bf{My\; Try::}$ Using $\bf{Cauchy\; Schwarz}$ Inequality
$$\frac{a^2}{a^2+2}+\frac{b^2}{b^2+2}+\frac{c^2}{c^2+2}\geq \frac{(a+b+c)^2}{a^2+b^2+c^2+6}$$
Now How can I solve after that, Help Required
Thanks
 [/INST] Plug in $c = \frac1{ab}$, and set the partial derivatives $\frac{\partial}{\partial a}$ and $\frac{\partial}{\partial b}$ equal to zero to find candidates for a minimum.
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