a.
\(\Leftrightarrow\sqrt[3]{3x-5}=\left(2x-3\right)^3+2x-3-\left(3x-5\right)\)
Đặt \(\left\{{}\begin{matrix}2x-3=a\\\sqrt[3]{3x-5}=b\end{matrix}\right.\)
\(\Rightarrow b=a^3+a-b^3\)
\(\Leftrightarrow a^3-b^3+a-b=0\)
\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)
\(\Leftrightarrow a=b\)
\(\Leftrightarrow\sqrt[3]{3x-5}=2x-3\)
\(\Leftrightarrow3x-5=\left(2x-3\right)^3\)
\(\Leftrightarrow8x^3-36x^2+51x-22=0\)
\(\Leftrightarrow\left(x-2\right)\left(8x^2-20x+11\right)=0\)
\(\Leftrightarrow...\)
b.
\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+3x-2-\sqrt[3]{81x-8}=0\)
\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+\dfrac{\left(3x-2\right)^3-\left(81x-8\right)}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}=0\)
\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x+\dfrac{27\left(x^3-2x^2-\dfrac{5}{3}x\right)}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}=0\)
\(\Leftrightarrow\left(x^3-2x^2-\dfrac{5}{3}x\right)\left(1+\dfrac{27}{\left(3x-2\right)^2+\left(3x-2\right)\sqrt[3]{81x-8}+\sqrt[3]{\left(81x-8\right)^2}}\right)=0\)
\(\Leftrightarrow x^3-2x^2-\dfrac{5}{3}x=0\)
c.
\(\Leftrightarrow\sqrt[3]{x-2}=\left(2x-5\right)^3+x-3\)
\(\Leftrightarrow\sqrt[3]{x-2}=\left(2x-5\right)^3+\left(2x-5\right)-\left(x-2\right)\)
Đặt \(\left\{{}\begin{matrix}2x-5=a\\\sqrt[3]{x-2}=b\end{matrix}\right.\)
\(\Rightarrow b=a^3+a-b^3\)
\(\Leftrightarrow a^3-b^3+a-b=0\)
\(\Leftrightarrow\left(a-b\right)\left(a^2+ab+b^2+1\right)=0\)
\(\Leftrightarrow a=b\)
\(\Leftrightarrow2x-5=\sqrt[3]{x-2}\)
\(\Leftrightarrow\left(2x-5\right)^3=x-2\)
\(\Leftrightarrow\left(x-3\right)\left(8x^2-36x+41\right)=0\)
