tinh nhanh 2009 x 7 + 2009 x 2 + 2009
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( - 2009 - 2009 - 2009 - 2009 ) . ( - 25 )
= 2009 + 2009 + 2009 + 2009 . ( - 25 )
= 2009 . 4 . ( - 25 )
= 2009 . [ 4 . ( - 25 ) ]
= 2009 . ( - 100 )
= - 200 900
(m+1 −m x 1 ) : 9m x 2009 +m +1)
=(m+1−m)÷(2010m+1)
=1÷(2010m+1)
=12010m+1
\(\dfrac{\left(2009-x\right)^2+\left(2009-x\right)\left(x-2010\right)+\left(x-2010\right)^2}{\left(2009-x\right)^2-\left(2009-x\right)\left(x-2010\right)+\left(x-2010\right)^2}=\dfrac{19}{49}\left(1\right)\)
\(Đkxđ:x\ne2009;x\ne2010\)
Đặt \(t=x-2010\left(t\ne0\right)\)
\(\Rightarrow2009-x=-\left(t+1\right)\)
\(\left(1\right)\Leftrightarrow\dfrac{\left(t+1\right)^2-\left(t+1\right)t+t^2}{\left(t+1\right)^2+\left(t+1\right)t+t^2}=\dfrac{19}{49}\)
\(\Leftrightarrow\dfrac{t^2+2t+1-t^2-t+t^2}{t^2+2t+1+t^2+t+t^2}=\dfrac{19}{49}\)
\(\Leftrightarrow\dfrac{t^2+t+1}{3t^2+3t+1}=\dfrac{19}{49}\)
\(\Leftrightarrow49t^2+49t+49=57t^2+57t+19\)
\(\Leftrightarrow8t^2+8t-30=0\)
\(\Leftrightarrow4t^2+4t-15=0\)
\(\Leftrightarrow\left(4t^2+4t+1\right)-16=0\)
\(\Leftrightarrow\left(2t+1\right)^2=16=4^2\)
\(\Leftrightarrow\left[{}\begin{matrix}2t+1=4\\2t+1=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}t=\dfrac{3}{2}\\t=-\dfrac{5}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x-2010=\dfrac{3}{2}\\x-2010=-\dfrac{5}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4023}{2}\\x=\dfrac{4015}{2}\end{matrix}\right.\)
2009 x 17 + 4018 x 41 + 2009 = 2009 x 17 + 2009 x (2 x 41) + 2009
= 2009 x 17 + 2009 x 52 + 2009 x 1
= 2009 x (17 + 52 +1)
= 2009 x 100
= 200900
2009 x 7 + 2009 x 2 + 2009
= 2009 x (7 + 2) + 2009
= 2009 x 9 + 2009
= 18081 + 2009
= 20090
hoặc : 2009 x 7 + 2009 x 2 + 2009
= 2009 x (7 + 2 + 1)
= 2009 x 10
= 20090
20090