Bài 1;giải phương trình sau; 5(3x + 2) = 4x +1
(x -3) (x + 4)=0
2/x +1 - 1/x -2= 3x -11/(x +1)(x - 2)
bài 2 Giải bài toán sau bằng cách lập phương trình: Một ôtô đi từ A đến B với vận tốc trung bình 50km/h. Lúc về, ôtô đi với vận tốc trung bình 60km/h, nên thời gian về ít hơn thời gian đi là 30 phút. Hỏi quãng đường AB dài bao nhiêu kilômét?
bài 3Giải phương trình sau:x-1/2013 + x-2/2012 + x-3/2011 = x-4/2010 +x-5/2009 + x-6/2008
Bài 3:
\(\dfrac{x-1}{2013}+\dfrac{x-2}{2012}+\dfrac{x-3}{2011}=\dfrac{x-4}{2010}+\dfrac{x-5}{2009}+\dfrac{x-6}{2008}\)
\(\Leftrightarrow\dfrac{x-1}{2013}-1+\dfrac{x-2}{2012}-1+\dfrac{x-3}{2011}-1-\dfrac{x-4}{2010}-1-\dfrac{x-5}{2009}-1-\dfrac{x-6}{2008}-1=0\)
\(\Leftrightarrow\dfrac{x-2014}{2013}+\dfrac{x-2014}{2012}+\dfrac{x-2014}{2011}-\dfrac{x-2014}{2010}-\dfrac{x-2014}{2009}-\dfrac{x-2014}{2008}=0\)
\(\Leftrightarrow\left(x-2014\right)\left(\dfrac{1}{2013}+\dfrac{1}{2012}+\dfrac{1}{2011}-\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\ne0\right)=0\)
\(\Leftrightarrow x-2014=0\)
\(\Leftrightarrow x=2014\)
Vậy PT có nghiệm là \(x=2014\)
Bài 1:
a) \(5\left(3x+2\right)=4x+1\)
\(\Rightarrow15x+10=4x+1\)
\(\Rightarrow11x=-9\)
\(\Rightarrow x=\dfrac{-9}{11}\)
Vậy \(x=\dfrac{-9}{11}\)
b) \(\left(x-3\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)
Vậy \(x\in\left\{3;-4\right\}\)
Bài 3:
\(\dfrac{x-1}{2013}+\dfrac{x-2}{2012}+\dfrac{x-3}{2011}=\dfrac{x-4}{2010}+\dfrac{x-5}{2009}+\dfrac{x-6}{2008}\)
\(\Rightarrow\left(\dfrac{x-1}{2013}-1\right)+\left(\dfrac{x-2}{2012}-1\right)+\left(\dfrac{x-3}{2011}-1\right)=\left(\dfrac{x-4}{2010}-1\right)+\left(\dfrac{x-5}{2009}-1\right)+\left(\dfrac{x-6}{2008}-1\right)\)
\(\Rightarrow\dfrac{x-2014}{2013}+\dfrac{x-2014}{2012}+\dfrac{x-2014}{2011}=\dfrac{x-2014}{2010}+\dfrac{x-2014}{2009}+\dfrac{x-2014}{2008}\)
\(\Rightarrow\dfrac{x-2014}{2013}+\dfrac{x-2014}{2012}+\dfrac{x-2014}{2011}-\dfrac{x-2014}{2010}-\dfrac{x-2014}{2009}-\dfrac{x-2014}{2008}=0\)
\(\Rightarrow\left(x-2014\right)\left(\dfrac{1}{2013}+\dfrac{1}{2012}+\dfrac{1}{2011}-\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\right)=0\)
Mà \(\dfrac{1}{2013}+\dfrac{1}{2012}+\dfrac{1}{2011}-\dfrac{1}{2010}-\dfrac{1}{2009}-\dfrac{1}{2008}\ne0\)
\(\Rightarrow x-2014=0\Rightarrow x=2014\)
Vậy x = 2014