Question

[Thái Xuân Đăng]

không có gì để hỏi

Answer 1

[Phạm Thế Mạnh]

\(\Leftrightarrow\sqrt[3]{x-5}+\sqrt[3]{2x-1}=\sqrt[3]{3x+2}-2\)
\(\Leftrightarrow3x-6+3\sqrt[3]{\left(x-5\right)\left(2x-1\right)}\left(\sqrt[3]{x-5}+\sqrt[3]{2x-1}\right)=3x+2-8-3.2\sqrt[3]{3x+2}\left(\sqrt[3]{3x+2}-2\right)\)
\(\Leftrightarrow3\sqrt[3]{\left(x-5\right)\left(2x-1\right)}\left(\sqrt[3]{3x+2}-2\right)=3.2\sqrt[3]{3x+2}\left(\sqrt[3]{3x+2}-2\right)\)
\(\Leftrightarrow\left(\sqrt[3]{3x+2}-2\right)\left(\sqrt[3]{\left(x-5\right)\left(2x-1\right)}+2\sqrt[3]{3x+2}\right)=0\)
\(\Leftrightarrow\int^{\sqrt[3]{3x+2}=2}_{\sqrt[3]{\left(x-5\right)\left(2x-1\right)}=-2\sqrt[3]{3x+2}}\)
\(\Leftrightarrow\int^{x=2}_{2x^2-11x+5=-24x-16}\)
\(\Leftrightarrow x\in\left\{2;-3;-3.5\right\}\)