Đáp án:
$H=2$
Giải thích các bước giải:
$H=\sqrt[3]{2+\dfrac{10}{3\sqrt{3}}}+\sqrt[3]{2-\dfrac{10}{3\sqrt{3}}}$
$⇔ H^3=2+\dfrac{10}{3\sqrt{3}}+2-\dfrac{10}{3\sqrt{3}}+3\sqrt[3]{(2+\dfrac{10}{3\sqrt{3}})(2-\dfrac{10}{3\sqrt{3}})}.(\sqrt[3]{2+\dfrac{10}{3\sqrt{3}}}+\sqrt[3]{2+\dfrac{10}{3\sqrt{3}}})$
$⇔ H^3=4+3\sqrt[3]{4-\dfrac{100}{27}}.H$
$⇔ H^3=4+3\sqrt[3]{\dfrac{8}{27}}.H$
$⇔ H^3=4+3.\dfrac{2}{3}.H$
$⇔ H^3-2H-4=0$
$⇔ H^3-2H^2+2H^2-4H+2H-4=0$
$⇔ (H-2)(H^2+2H+2)=0$
$\text{Vì $H^2+2H+2=(H+1)^2+1 > 0$}$
$\text{nên $H-2=0$}$
$⇔ H=2$
