$y=\frac{x^2}{(x^2+1+1)^3} \le \frac{x^2}{(3\sqrt[3]{x^2})^3}=\frac 1{27}$$\Rightarrow y_{max}=\frac 1{27}\Leftrightarrow x=1$
$y=\frac{x^2}{(x^2+1+1)^3} \le \frac{x^2}{(3\sqrt[3]{x^2})^3}=\frac 1{27}$$\Rightarrow y_{max}=1\Leftrightarrow x=1$
$y=\frac{x^2}{(x^2+1+1)^3} \le \frac{x^2}{(3\sqrt[3]{x^2})^3}=\frac 1{27}$$\Rightarrow y_{max}=
\frac 1
{27}\Leftrightarrow x=1$