Lời giải:
a)
\(|3x-1|=|2x-3|\)
\(\Rightarrow \left[\begin{matrix} 3x-1=2x-3\\ 3x-1=-(2x-3)\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=-2\\ x=\frac{4}{5}\end{matrix}\right.\)
b)
\((x-1)^4-3(x^2-2x)-7=0\)
\(\Leftrightarrow (x-1)^4-3(x^2-2x+1)-4=0\)
\(\Leftrightarrow (x-1)^4-3(x-1)^2-4=0\)
\(\Leftrightarrow a^2-3a-4=0\) (đặt \((x-1)^2=a\) )
\(\Leftrightarrow (a-4)(a+1)=0\)
\(\Rightarrow a=4\) (do $a=(x-1)^2\geq 0$)
\(\Rightarrow (x-1)^2=4\)
\(\Rightarrow \left[\begin{matrix} x-1=2\\ x-1=-2\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=3\\ x=-1\end{matrix}\right.\)
a) \(\left|3x-1\right|=\left|2x-3\right|\) <=> \(\left[{}\begin{matrix}3x-1=2x-3\\3x-1=-2x+3\end{matrix}\right.\) <=>\(\left[{}\begin{matrix}x=-2\\x=\dfrac{4}{5}\end{matrix}\right.\)
