Question

Nếu ( x-2)(2x - 4) - (2x + 4)( x-2) = ax² - bx - c thì giá trị của a là bao nhiêu?

Answer 1

\(\left(x-2\right)\left(2x-4\right)-\left(2x+4\right)\left(x-2\right)=ax^{2\: }-bx+c\)

\(\Leftrightarrow\left(x-2\right)\left(2x-4-2x+4\right)=ax^{2\:}-bx-c\)

\(\Leftrightarrow-8\left(x-2\right)=ax^{2\:}-bx-c\)

\(\Leftrightarrow ax^{2\:}-bx-c=-8x+16\)

\(\Leftrightarrow\left\{{}\begin{matrix}ax^{2\: }=0\\-bx=-8x\\-c=16\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=0\\b=8\\c=-16\end{matrix}\right.\)

Vậy a = 0