\(\frac{4}{3}\) x\(\frac{2011}{2011}\) +\(\frac{23}{8}\) = ? , làm ơn giúp mình các bạn nhé !
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\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
<=> \(\left(\frac{x-152}{2011}-1\right)+\left(\frac{x-2135}{28}-1\right)+\left(\frac{x-2039}{124}-1\right)=0\)
<=> \(\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)
<=> \(\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)
<=> \(x-2163=0\)(vì \(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\ne0\)
<=> \(x=2163\)
\(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
<=> \(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}-3=0\)
<=> \(\left(\frac{x-28-124}{2011}-1\right)+\left(\frac{x-124-2011}{28}-1\right)+\left(\frac{x-2011-28}{124}-1\right)=0\)
<=> \(\frac{x-28-124-2011}{2011}+\frac{x-124-2011-28}{28}+\frac{x-2011-28-124}{124}=0\)
<=> \(\frac{x-2163}{2011}+\frac{x-2163}{28}+\frac{x-2163}{124}=0\)
<=> \(\left(x-2163\right)\left(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\right)=0\)
Vì \(\frac{1}{2011}+\frac{1}{28}+\frac{1}{124}\ne0\)
=> \(x-2163=0\)
=> \(x=2163\)
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Ta có:\(\frac{x-1}{2013}+\frac{x-2}{2012}=\frac{x-3}{2011}+\frac{x-4}{2010}\)
\(\Rightarrow\left(\frac{x-1}{2013}-1\right)+\left(\frac{x-2}{2012}-1\right)=\left(\frac{x-3}{2011}-1\right)+\left(\frac{x-4}{2010}-1\right)\)
\(\Rightarrow\frac{x-2014}{2013}+\frac{x-2014}{2012}=\frac{x-2014}{2011}+\frac{x-2014}{2010}\)
\(\Rightarrow\frac{x-2014}{2013}+\frac{x-2014}{2012}-\frac{x-2014}{2011}-\frac{x-2014}{2010}=0\)
\(\Rightarrow\left(x-2014\right).\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)
Vì \(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\ne0\)nên để biểu thức =0
\(\Leftrightarrow x-2014=0\Rightarrow x=2014\)
Ta cTa có: 2013 x − 1 + 2012 x − 2 = 2011 x − 3 + 2010 x − 4 ⇒ 2013 x − 1 − 1 + 2012 x − 2 − 1 = 2011 x − 3 − 1 + 2010 x − 4 − 1 ⇒ 2013 x − 2014 + 2012 x − 2014 = 2011 x − 2014 + 2010 x − 2014 ⇒ 2013 x − 2014 + 2012 x − 2014 − 2011 x − 2014 − 2010 x − 2014 = 0 ⇒ x − 2014 . 2013 1 + 2012 1 − 2011 1 − 2010 1 = 0
1 = 0
chúc bn hok tốt @_@
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\(\frac{2011^{2011}+2}{2011^{2011}-1}=\frac{2011^{2011}-1+3}{2011^{2011}-1}=1+\frac{3}{2011^{2011}-1}\)
\(\frac{2011^{2011}}{2011^{2011}-3}=\frac{2011^{2011}-3+3}{2011^{2011}-3}=1+\frac{3}{2011^{2011}-3}\)
Vì 1 = 1 và \(\frac{3}{2011^{2011}-1}>\frac{3}{2011^{2011}-3}\)nên \(1+\frac{3}{2011^{2011}-1}>1+\frac{3}{2011^{2011}-3}\)hay \(A>B\)
Vậy \(A>B\)
-So sánh B với A
B>1 ( tử lớn hơn mẫu ) => B> 20112011+2/20112011-3+2 => B> 20112011+2/20112011+ -1 =A
=> B > A => A < B.
(Bài trên dựa vào cách sau : Nếu a/b > 1 => a/b > a+m/b+m (m thuộc N*) và nếu a/b <1 thì ngược lại)
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\(\frac{x+4}{2009}+\frac{x+3}{2010}=\frac{x+2}{2011}+\frac{x+1}{2012}\)\(\Leftrightarrow\)\(\left(\frac{x+4}{2009}+1\right)+\left(\frac{x+3}{2010}+1\right)=\left(\frac{x+2}{2011}+1\right)+\left(\frac{x+1}{2012}+1\right)\)
\(=\frac{x+2013}{2009}+\frac{x+2013}{2010}=\frac{x+2013}{2011}+\frac{x+2013}{2012}\)
Biểu thức trên chi thỏa mãn khi x+2013=0
\(\Rightarrow x=-2013\)
mk nghĩ là -2013 vì nếu thay x=-2013 vào thì các phân số sẽ bằng -1.
nếu cộng lại thì đc -2
k nhé
Nhanh lên sắp 5 giờ rồi , HU HU