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Ta có : \(4x-\left(2x+1\right)=3-\frac{1}{3}+x\)
(=) \(4x-2x-1=3-\frac{1}{3}+x\)
(=) \(4x-2x-x=3-\frac{1}{3}+1\)
(=) \(x=\frac{11}{3}\)
\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{2011}\left(1+2+3+...+2011\right)\)
\(=1+\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+...+\frac{1}{2011}\cdot\frac{2011.2012}{2}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{2012}{2}\)
\(=\frac{2+3+4+...+2012}{2}\)
\(=\frac{\frac{2012\cdot2013}{2}-1}{2}=\frac{2025077}{2}\)
20-/y-2/=4(x-1)^4
20-4(x-1)^4=/y-2/
do/y-2/_>0 => 20-4(x-1)_>0
=>20_>4(x-1)^4
=>5_>(x-1)^4
=>(x-1)^4=1^4 hoac 0^4
=>x=2 hoac x=1
Ta có: B=1/199+2/198+3/197+...+197/3+198/2+199/1
= (1/199+1)+(2/198+1)+(3/197+1)+...+(197/3+1)+(198/2+1)+200/200
=200/199+200/198+200/197+...+200/3+200/2+200/1+200/200
=200( 1/200+1/199+1/198+1/197+...+1/3+1/2)
=200*A
=> A/B=A/200A=1/200
2^2002^199-2^198-2^197-....-2-1 giải giúp mình với toán lớp 6 đó đề học sinh giỏi nhé
\(\left(x-2011\right)^{x+1}-\left(x-2011\right)^{x+2011}=0\)
\(\left(x-2011\right)^{x+1}\left[1-\left(x-2011\right)^{2010}\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-2011\right)^{x+1}=0\\1-\left(x-2011\right)^{2010}=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-2011=0\\\left(x-2011\right)^{2010}=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2011\\x-2011=-1;1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2011\\x=2010;2012\end{cases}}\)
Vậy \(x=2010;2011;2012\)
(x - 2011)x +1 - (x - 2011)x + 2011 = 0
ta có : x - 2011 = 0 => x= 2011
a) \(\left(x-\dfrac{1}{2}\right)^2=0\)
\(\Rightarrow x-\dfrac{1}{2}=0\)
\(\Rightarrow x=\dfrac{1}{2}\)
b) \(\left(x-2\right)^2=1\)
\(\Rightarrow x-2=1\)
\(\Rightarrow x=3\)
c) \(\left(2x-1\right)^3=-8\)
\(\Rightarrow\left(2x-1\right)^3=\left(-2\right)^3\)
\(\Rightarrow2x-1=-2\)
\(\Rightarrow2x=-1\)
\(\Rightarrow x=\dfrac{-1}{2}\)
d) \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow\left(x+\dfrac{1}{2}\right)^2=\left(\dfrac{1}{4}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{matrix}\right.\).
a , \(\left(x-\dfrac{1}{2}\right)^2=0\)
<=> \(x-\dfrac{1}{2}=0\Rightarrow x=\dfrac{1}{2}\)
b , \(\left(x-2\right)^2=1\Rightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
c , \(\left(2x-1\right)^3=-8\Rightarrow2x-1=-2\Rightarrow x=\dfrac{-1}{2}\)
d , \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{4^2}\)
<=> \(\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=\dfrac{-1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{4}\\x=\dfrac{-3}{4}\end{matrix}\right.\)