\(pt\Leftrightarrow x-1+x-3+3\sqrt[3]{\left(x-1\right)\left(x-3\right)}\left(\sqrt[3]{x-1}+\sqrt[3]{x-3}\right)=2x-3\)
\(\Leftrightarrow3\sqrt[3]{\left(x-1\right)\left(x-3\right)}\left(\sqrt[3]{x-1}+\sqrt[3]{x-3}\right)=1\)
\(\Rightarrow3\sqrt[3]{\left(x-1\right)\left(x-3\right)}.\sqrt[3]{2x-3}=1\)
\(\Leftrightarrow27\left[\left(x-1\right)\left(x-3\right)\left(2x-3\right)\right]=1\)
\(\Leftrightarrow27\left(2x^3-11x^2+18x-9\right)=1\)
\(\Leftrightarrow54x^3-297x^2+486x-244=0\)
Đến đây chịu, đề có sai sót gì không, t đoán đề là \(\sqrt[3]{x-1}+\sqrt[3]{x-2}=\sqrt[3]{2x-3}\) (đoán thôi).
