1/2 * x + 1/5 * x + 0.3x = 2014
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\(a,\left(\frac{15}{10}x+25\right):\frac{2}{3}=60\)
\(\Rightarrow\frac{15}{10}x+25=60.\frac{2}{3}\)
\(\Rightarrow\frac{15}{10}x+25=40\)
\(\Rightarrow\frac{15}{10}x=40-25\)
\(\Rightarrow\frac{15}{10}x=15\)
\(\Rightarrow x=15:\frac{15}{10}\)
\(\Rightarrow x=15.\frac{10}{15}\)
\(\Rightarrow x=10\)
=> (x+2020)/5=(x+2020)/6=(x+2020)/3+(x+2020)/2
=>(x+2020)(1/5+1/6)=(x+2020)(1/3+1/2)
Với x+2020=0=>x=-2020
Với x+2020 khác 0=>1/5+1/6=1/3+1/2 ,vô lí
Vậy x=-2020
1).x:2+x:3=5/2
=>x.1/2+x.1/3=5/2
=>x(1/2+1/3)=5/2
=>x.5/6=5/2
=>x=5/2:5/6
=>x=3
Bạn xem lại đề câu a) cho rõ lại
Câu b) Tại x=2013 thì B=x2013-(x+1)x2012+(x+1)x2011-(x+1)x2010+...-(x+1)x2+(x+1)x-1
= x2013-x2013-x2012+x2012+x2011-x2011-x2010+..-x3 - x2+x2+x-1
= x-1 = 2012
Ta có: \(\left(2x-1\right)^{2014}+\left(y-\dfrac{2}{5}\right)^{2014}+\left|x+y+z\right|=0\)
\(\Rightarrow\left(2x-1\right)^{2014}=0\) (1)
\(\Rightarrow\left(y-\dfrac{2}{5}\right)^{2014}=0\) (2)
\(\Rightarrow\left|x+y+z\right|=0\) (3)
(1) Ta tìm được x:
\(\left(2x-1\right)^{2014}=0\)
\(\Rightarrow2x-1=0\)
\(\Rightarrow2x=1\)
\(\Rightarrow x=\dfrac{1}{2}\)
(2) Ta tìm được y:
\(\left(y-\dfrac{2}{5}\right)^{2014}=0\)
\(\Rightarrow y-\dfrac{2}{5}=0\)
\(\Rightarrow y=\dfrac{2}{5}\)
Từ (1) và (2) ta kết hợp với (3) ta sẽ tìm được z:
\(x+y+z=0\) hay \(\dfrac{1}{2}+\dfrac{2}{5}+z=0\)
\(\Rightarrow\dfrac{9}{10}+z=0\)
\(\Rightarrow z=-\dfrac{9}{10}\)
Vậy: \(x=\dfrac{1}{2};y=\dfrac{2}{5};z=-\dfrac{9}{10}\)
\(\left(2x-1\right)^{2014}+\left(y-\dfrac{2}{5}\right)^{2014}+|x+y+z|=0\left(1\right)\)
mà \(\left(2x-1\right)^{2014}\ge0;\left(y-\dfrac{2}{5}\right)^{2014}\ge0\) (với mọi x;y)
\(\left(1\right)\Rightarrow2x-1=0;y-\dfrac{2}{5}=0;|x+y+z|=0\)
\(\Rightarrow x=\dfrac{1}{2};y=\dfrac{2}{5};z=-\dfrac{1}{2}-\dfrac{2}{5}=-\dfrac{9}{10}\)
\(\left\{{}\begin{matrix}0,3x+0,5y=3\\1,5x-2y=1,5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}1,5x+2,5y=15\\1,5x-2y=1,5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4,5y=13,5\\1,5x-2y=1,5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\1,5x=2y+1,5=2\cdot3+1,5=7,5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=5\\y=3\end{matrix}\right.\)
\(\left\{{}\begin{matrix}0,3x+0,5y=3\\1,5x-2y=1,5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}1,5x+2,5y=15\\1,5x-2y=1,5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}4,5y=-13,5\\1,5x-2y=1,5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-13,5}{4,5}=3\\1,5x-2.3=1,5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{1,5+6}{1,5}=5\end{matrix}\right.\\ Vậy:\left(x;y\right)=\left(5;3\right)\)
\(\dfrac{1}{2}\cdot x+\dfrac{1}{5}\cdot x+0,3\cdot x=2014\)
=>\(x\left(0,5+0,2+0,3\right)=2014\)
=>\(x\cdot1=2014\)
=>x=2014