Question

Cac bạn giúp mình 4 câu này:

1). X² - 2003x - 2004 = 0

2). 2005x² - 2004x - 1 = 0

Giúp mình nha!

Answer 1

1, \(x^2-2003x-2004=0\)

\(\Rightarrow x^2+x-\left(2004x+2004\right)=0\)

\(\Rightarrow x\left(x+1\right)-2004\left(x+1\right)=0\)

\(\Rightarrow\left(x-2004\right)\left(x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-2004=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2004\\x=-1\end{matrix}\right.\)

Vậy x = 2004 hoặc x = -1

2, \(2005x^2-2004x-1=0\)

\(\Rightarrow2005x^2-2005x+x-1=0\)

\(\Rightarrow2005x\left(x-1\right)+\left(x-1\right)=0\)

\(\Rightarrow\left(2005x+1\right)\left(x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2005x+1=0\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{2005}\\x=1\end{matrix}\right.\)

Vậy \(x=\dfrac{-1}{2005}\) hoặc x = 1