Question

Giải phương trình bằng cách đặt ẩn phụ:

a) ( 2x² - 3x - 1)² - 3( 2x² - 3x - 5 ) - 16 = 0

b) 8( x² + \(\dfrac{1}{x^2}\) ) - 34( x + \(\dfrac{1}{x}\) ) + 51 = 0

Answer 1

a) Đặt \(2x^2-3x-1=a\)

Bt \(\Leftrightarrow a^2-3\left(a-4\right)-16=0\)

\(\Leftrightarrow a^2-3a+12-16=0\)

\(\Leftrightarrow\left(a-4\right)\left(a+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-1=4\\2x^2-3x-1=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-5=0\\2x^2-3x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x+1\right)\left(2x-5\right)=0\\x\left(2x-3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=-1\\x=2.5\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\x=1.5\end{matrix}\right.\end{matrix}\right.\)