1.
PT \(\Leftrightarrow (x+2)(x-3)(x-4)(x+6)=16x^2\)
\(\Leftrightarrow [(x+2)(x+6)][(x-3)(x-4)]=16x^2\)
\(\Leftrightarrow (x^2+8x+12)(x^2-7x+12)=16x^2\)
\(\Leftrightarrow (a+8x)(a-7x)=16x^2\) (đặt \(x^2+12=a\) )
\(\Leftrightarrow a^2+ax-72x^2=0\)
\(\Leftrightarrow (a-8x)(a+9x)=0\Rightarrow \left[\begin{matrix} a-8x=0\\ a+9x=0\end{matrix}\right.\)
Nếu \(a-8x=0\Leftrightarrow x^2+12-8x=0\Leftrightarrow (x-2)(x-6)=0\Rightarrow \left[\begin{matrix} x=2\\ x=6\end{matrix}\right.\)
Nếu \(a+9x=0\Leftrightarrow x^2+12+9x=0\Leftrightarrow x=\frac{-9\pm \sqrt{33}}{2}\)
Vậy...........
2.
PT \(\Leftrightarrow [(4x+7)(2x+1)][(4x+5)(x+1)]=9\)
\(\Leftrightarrow (8x^2+18x+7)(4x^2+9x+5)=9\)
\(\Leftrightarrow (2a+7)(a+5)=9\) (đặt \(a=4x^2+9x\) )
\(\Leftrightarrow 2a^2+17a+26=0\)
\(\Leftrightarrow (a+2)(2a+13)=0 \)\(\Rightarrow \left[\begin{matrix} a+2=0\\ 2a+13=0\end{matrix}\right.\)
Nếu \(a+2=0\Leftrightarrow 4x^2+9x+2=0\Leftrightarrow (4x+1)(x+2)=0\)
\(\Rightarrow \left[\begin{matrix} x=\frac{-1}{4}\\ x=-2\end{matrix}\right.\)
Nếu \(2a+13=0\Leftrightarrow 8x^2+18x+13=0\) (pt này dễ thấy vô nghiệm)
Vậy.........
3.
PT \(\Leftrightarrow (16x^2-40x+25)(2x^2-5x+3)=1,5\)
\(\Leftrightarrow [8(2x^2-5x)+25](2x^2-5x+3)=1,5\)
\(\Leftrightarrow (8a+25)(a+3)=1,5\) (đặt \(a=2x^2-5x\))
\(\Leftrightarrow 8a^2+49a+73,5=0\)
\(\Leftrightarrow 16a^2+98a+147=0\)
\(\Leftrightarrow (8a+21)(2a+7)=0\) \(\Rightarrow \left[\begin{matrix} 8a+21=0\\ 2a+7=0\end{matrix}\right.\)
Nếu \(8a+21=0\Leftrightarrow 16x^2-40x+21=0\)
\(\Leftrightarrow (4x-7)(4x-3)=0\Rightarrow \left[\begin{matrix} x=\frac{7}{4}\\ x=\frac{3}{4}\end{matrix}\right.\)
