Câu a:
\(2x\left(8x-1\right)^2\left(4x-1\right)=9\)
\(\Leftrightarrow\left(64x^2-16x+1\right)\left(64x^2-16x\right)=72\)
Đặt 64x2 - 16x = t \(\left(t\ge-1\right)\)
\(\Rightarrow t\left(t+1\right)=72\)
\(\Leftrightarrow\left(t+9\right)\left(t-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=-9\left(loai\right)\\t=8\left(nhan\right)\end{matrix}\right.\)
\(\Rightarrow64x^2-16x=8\)
\(\Leftrightarrow8\left(2x-1\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
Câu b:
\(\Leftrightarrow\left(x+1\right)^2\left(2x+1\right)\left(2x+3\right)=18\)
\(\Leftrightarrow\left(4x^2+8x+4\right)\left(4x^2+8x+3\right)=72\)
Đặt 4x2 + 8x + 4 = m \(\left(m\ge0\right)\)
\(\Rightarrow m\left(m-1\right)=72\)
\(\Leftrightarrow\left(m-9\right)\left(m+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}m=9\left(nhan\right)\\m=-8\left(loai\right)\end{matrix}\right.\)
\(\Rightarrow4\left(x+1\right)^2=9\)
\(\Leftrightarrow x+1=\pm\dfrac{3}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)