\(\left(\sqrt[3]{2x-1}+\sqrt[3]{x-1}\right)^3=x\)
\(\Leftrightarrow2x-1+x-1+3\left(\sqrt[3]{2x-1}\right)^2\sqrt[3]{x-1}+3\sqrt[3]{2x-1}.\left(\sqrt[3]{x-1}\right)^2=x\)
\(\Leftrightarrow3\sqrt[3]{2x-1}\sqrt[3]{x-1}.\left(\sqrt[3]{2x-1}+\sqrt[3]{x-1}\right)=2-2x\)
\(\Leftrightarrow3\sqrt[3]{2x-1}\sqrt[3]{x-1}.\sqrt[3]{x}=2-2x\)
\(\Leftrightarrow\left(3\sqrt[3]{2x-1}\sqrt[3]{x-1}.\sqrt[3]{x}\right)^3=\left(2-2x\right)^3\)
\(\Leftrightarrow27x\left(x-1\right)\left(2x-1\right)=8\left(1-x\right)^3\)
\(\Leftrightarrow27x\left(x-1\right)\left(2x-1\right)+8\left(x-1\right)^3=0\)
\(\Leftrightarrow\left(x-1\right)\left(27x\left(2x-1\right)+8\left(x-1\right)^2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(54x-27+8\left(x^2-2x+1\right)\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(54x-27+8x^2-16x+8\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(8x^2+38x-19\right)=0\)
tới đây tìm đc x
