Question

\(\left(8x-7\right)\left(8x-5\right)\left(2x-1\right)\left(4x-1\right)=9\)

Answer 1

Lời giải:

PT \(\Leftrightarrow [(8x-7)(4x-1)][(8x-5)(2x-1)]=9\)

\(\Leftrightarrow (32x^2-36x+7)(16x^2-18x+5)=9\)

Đặt \(16x^2-18x=a\). PT trở thành:

\((2a+7)(a+5)=9\)

\(\Leftrightarrow 2a^2+17a+26=0\)

\(\Rightarrow \left[\begin{matrix} a=-2\\ a=\frac{-13}{2}\end{matrix}\right.\)

\(a=-2\Leftrightarrow 16x^2-18x+2=0\)

\(\Leftrightarrow (8x-1)(x-1)=0\Rightarrow \left[\begin{matrix} x=1\\ x=\frac{1}{8}\end{matrix}\right.\)

\(a=\frac{-13}{2}\Leftrightarrow 16x^2-18x+\frac{13}{2}=0\) (pt vô nghiệm)

Vậy............