2012=|x-2010|+|x-2008|
Những câu hỏi liên quan
x-2012/2008-x-2012/2009=x-2012/2010-x-2012/2011.tìm x
(6/2008*2010+6/2010*2012+6/2012*2014+6/2014*2016+6/2016*2018)+3/x=3/2008
Cho x=2011.Tính GTBT:
A= \(x^{2011}-2012.x^{2010}+2012.x^{2009}-2012.x^{2008}+...-2012.x^2+2012.x-1^{ }\)
Ta có: x=2011 \(\Rightarrow\)x+1=2012
\(\Rightarrow A=x^{2011}-\left(x+1\right).x^{2010}\)\(+\left(x+1\right)x^{2009}\)\(-\left(x+1\right)x^{2008}+...\)\(-\left(x+1\right)x^2+\left(x+1\right)x-1\)
=\(x^{2011}\)\(-x^{2011}-x^{2010}+x^{2010}+x^{2009}-x^{2009}-\)...\(-x^2+x^2+x-1\)
= \(x-1=2011-1=2010\)
=
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Thay 2012=x+1.
\(A=x^{2011}-\left(x+1\right)x^{2010}+\left(x+1\right)x^{2009}-\left(x+1\right)x^{2008}+...-\left(x+1\right)x^2+\left(x+1\right)x-1\)
\(A=x^{2011}-x^{2011}-x^{2010}+x^{2010}+x^{2009}-...-x^3-x^2+x^2+x-1\)
\(A=x-1=2011-1=2010\)
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1. Tìm x biết: 2012 = | x-2010 | + | x-2008 |
2. Cho A = | x-2010 | + | x-2012 | | x-2014 |
Tìm x để A đạt GTNN
tìm x
2012=/x-2010/+/x-2008/
+) Xét \(x\ge2010\) có:
\(2012=x-2010+x-2008\)
\(\Rightarrow2x-4018=2012\)
\(\Rightarrow2x=6030\)
\(\Rightarrow x=3015\) ( t/m )
+) Xét \(2008\le x< 2010\) ta có:
\(2012=2010-x+x-2008\)
\(\Rightarrow2=2012\) ( loại )
+) Xét \(x< 2008\) có:
\(2012=2010-x+2008-x\)
\(\Rightarrow2012=4018-2x\)
\(\Rightarrow2x=2006\)
\(\Rightarrow x=1003\left(tm\right)\)
Vậy x= 3015 hoặc x = 1003
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Tìm x y z biết:
2012=|x-2010|+|x-2008|
x-1 / 2013 + x-2 / 2012 + x-3 / 2011 = x-4 / 2010 + x-5 / 2009 + x-6 / 2008
\(\dfrac{x-1}{2013}+\dfrac{x-2}{2012}+\dfrac{x-3}{2011}=\dfrac{x-4}{2010}+\dfrac{x-5}{2009}+\dfrac{x-6}{2008}\)
\(\Leftrightarrow\dfrac{x-1}{2013}-1+\dfrac{x-2}{2012}-1+\dfrac{x-3}{2011}-1=\dfrac{x-4}{2010}-1+\dfrac{x-5}{2009}-1+\dfrac{x-6}{2008}-1\)
=>x-2014=0
hay x=2014
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tổng các nghiệm của phương trình (x-2010)(x-2009)(x-2008)...(x+2011)(x+2012)(x+2013)=0 bằng ?
Tìm x biết: (x+1/2013) + (x+2/2012) + (x+3/2011) = (x+4/2010) + (x+5/2009) + (x+6/2008)
`Answer:`
\(\left(\frac{x+1}{2013}\right)+\left(\frac{x+2}{2012}\right)+\left(\frac{x+3}{2011}\right)=\left(\frac{x+4}{2010}\right)+\left(\frac{x+5}{2009}\right)+\left(\frac{x+6}{2008}\right)\)
\(\Leftrightarrow\frac{x+1}{2013}+1+\frac{x+2}{2012}+1+\frac{x+3}{2011}+1=\frac{x+4}{2010}+1+\frac{x+5}{2009}+1+\frac{x+6}{2008}+1\)
\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}=\frac{x+2014}{2010}+\frac{x+2014}{2009}+\frac{x+2014}{2008}\)
\(\Leftrightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}+\frac{x+2014}{2011}-\frac{x+2014}{2010}-\frac{x+2014}{2009}-\frac{x+2014}{2008}=0\)
\(\Leftrightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}-\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)
\(\Rightarrow x+2014=0\)
\(\Leftrightarrow x=-2014\)