Giải thích các bước giải:
a.Ta có
$h(x)=\dfrac{x}{4}+\dfrac{x}{4}+\dfrac{x}{4}+\dfrac{x}{4}+\dfrac{1}{x}+\dfrac{1}{x}+\dfrac{1}{x}$
$\to h(x)\ge \dfrac{x}{4}+6\sqrt[6]{\dfrac{x}{4}.\dfrac{x}{4}.\dfrac{x}{4}.\dfrac{1}{x}.\dfrac{1}{x}.\dfrac{1}{x}}$
$\to h(x)\ge \dfrac{2}{4}+3=\dfrac{7}{2}$
Dấu = xảy ra khi $x=2$
b.$k(x)=x+x+\dfrac{1}{8x^2}+\dfrac{7}{8x^2}\ge 3\sqrt[3]{x.x.\dfrac{1}{8x^2}}+\dfrac{7}{8.\dfrac{1}{2}^2}=5$
Dấu = xảy ra khi $x=\dfrac 12$