Đặt : $E = \sqrt[3]{{{\rm{a}}{{\rm{x}}^2} + b{y^2} + c{{\rm{z}}^2}}} =
\sqrt[{3}]{{\frac{{{\rm{a}}{{\rm{x}}^3}}}{x} + \frac{{b{y^3}}}{y} +
\frac{{c{{\rm{z}}^3}}}{z}}}$
$ = \sqrt[3]{{\frac{{{\rm{a}}{{\rm{x}}^3}}}{x} + \frac{{{\rm{a}}{{\rm{x}}^3}}}{y}
+ \frac{{{\rm{a}}{{\rm{x}}^3}}}{z}}} = \sqrt[3]{{{\rm{a}}{{\rm{x}}^3}\left( {\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} \right)}} = x\sqrt[3]{a}$
$\Rightarrow\frac{\sqrt[3]{a}}{\sqrt[3]{ax^2+by^2+cz^2}}=\frac{1}{x}$
Tương tự :
$\frac{\sqrt[3]{b}}{\sqrt[3]{ax^2+by^2+cz^2}}=\frac{1}{y}$
$\frac{\sqrt[3]{c}}{\sqrt[3]{ax^2+by^2+cz^2}}=\frac{1}{z}$
$\Rightarrow\frac{\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}}{\sqrt[3]{ax^2+by^2+cz^2}}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1$
$\Rightarrow $ Kết quả