[TEX]\sqrt[3]{x-1}+\sqrt[3]{x-2}=\sqrt[3]{2x-1}[/TEX](lập phương)
[TEX]\Rightarrow x-1+x-2+3(\sqrt[3]{x-1})(\sqrt[3]{x-2})(\sqrt[3]{x-1}+\sqrt[3]{x-2})=2x-1[/TEX]
[TEX]\Rightarrow x-1+x-2+3(\sqrt[3]{x-1})(\sqrt[3]{x-2})(\sqrt[3]{2x-1})=2x-1[/TEX]
(do [TEX]\sqrt[3]{x-1}+\sqrt[3]{x-2}=\sqrt[3]{2x-1}[/TEX])
[TEX]\Rightarrow2=3(\sqrt[3]{x-1})(\sqrt[3]{x-2})(\sqrt[3]{2x-1})[/TEX](lập phương)
[TEX]\Rightarrow 8=27(2x^3-7x^2+7x-2)[/TEX]
[TEX]\Rightarrow 54x^3-189x^2+189x-62=0[/TEX](bấm máy tính ra nghiệm nha,rồi thử lại)