Đáp án:
$\max\left(\dfrac{x^2}{x^4 - x^2+1}\right)= 1 \Leftrightarrow x =\pm 1$
Giải thích các bước giải:
$\quad M =\dfrac{x^2}{x^4 - x^2+1}$
$+)\quad x = 0\Rightarrow M = 0$
$+)\quad x\ne 0$
$\Rightarrow M =\dfrac{1}{x^2 - 1+\dfrac{1}{x^2}}$
$\Rightarrow M \leqslant \dfrac{1}{2\sqrt{x^2\cdot \dfrac{1}{x^2}} - 1}$
$\Rightarrow M\leqslant \dfrac{1}{2-1}= 1$
Dấu $=$ xảy ra $\Leftrightarrow x^2 =\dfrac{1}{x^2}\Leftrightarrow x =\pm 1$
Vậy $\max\left(\dfrac{x^2}{x^4 - x^2+1}\right) = 1 \Leftrightarrow x =\pm 1$
