Để mình giải chi tiết ra cho nha
Đặt $ax^3=by^3=cz^3=k^3 => a=\frac{k^3}{x^3}; b=\frac{k^3}{y^3}; c^3=\frac{k^3}{z^3} => \sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}=\sqrt[3]{\frac{k^3}{x^3}}+\sqrt[3]{\frac{k^3}{y^3}}+\sqrt[3]{\frac{k^3}{z^3}}= \frac{k}{x}+\frac{k}{y}+\frac{k}{z}= k\left (\frac{1}{x} +\frac{1}{y}+ \frac{1}{z} \right )=k$
$\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{\frac{k^3x^2}{x^3}+\frac{k^3y^2}{y^3}+\frac{k^3z^2}{z^3}}=\sqrt[3]{\frac{k^3}{x}+\frac{k^3}{y}+\frac{k^3}{z}}= \sqrt[3]{k^3\left ( \frac{1}{x}+ \frac{1}{y}+ \frac{1}{z}\right )}=\sqrt[3]{k^3}=k$
$=> \sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}=\sqrt[3]{ax^3+by^2+cz^2}=k$
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