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\(=\frac{\left(379-2\right).733+722}{379.733-744}=\frac{379.733-1466+722}{379.733-744}=\frac{379.733-744}{379.733-744}=1\)
\(\frac{377.733+722}{379.733-744}\)
<=>\(\frac{277062}{277063}\)
\(\approx0,99\)
\(\frac{377.733+722}{379.733-744}\)=\(\frac{377+722}{379-744}\)
tích đúng cho mk nhé
gọi biểu thức trên là A.
\(B=\frac{377\cdot733+722}{379\cdot733-744}\)
\(=\frac{377\cdot733+722}{377\cdot733+733\cdot2-744}\)
\(=\frac{377\cdot733+722}{377\cdot733+\left(733\cdot2-744\right)}=\frac{377\cdot733+722}{377\cdot733+722}\)
= 1
\(\Rightarrow A=1+3\cdot\left(-4\right)^3-5\cdot\left(-2\right)^5\)
= 1+ (-192) - (-160)
= -31
=\(\dfrac{1}{2009.\left(\dfrac{1}{2009}+\dfrac{1}{2011}+\dfrac{1}{2010}\right)}+\dfrac{1}{2010.\left(\dfrac{1}{2010}+\dfrac{1}{2009}+\dfrac{1}{2011}\right)}+\dfrac{1}{2011.\left(\dfrac{1}{2011}+\dfrac{1}{2009}+\dfrac{1}{2010}\right)}\)\(=\dfrac{1}{2009}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2010}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2011}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)\)
\(=\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right):\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)=1\)
Ta có :
\(B=\frac{2008+2009+2010}{2009+2010+2011}=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
Vì :
\(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)
\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
Nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
\(\Rightarrow\)\(A>B\)
Vậy \(A>B\)
Ta có: \(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
Vì \(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)
\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008+2009+2010}{2009+2010+2011}\)
hay A > B
Vậy A > B
\(B=\dfrac{2008+2009+2010}{2009+2010+2011}=\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)Ta có : \(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)
\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)
\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)\(=>\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}>\dfrac{2008+2009+2010}{2009+2010+2011}\)
Hay A > B
P=\(\dfrac{2010\left(2010+1\right)-1}{2010^2+2009}+\dfrac{744-\left[\left(377+2\right).733\right]}{377.733+722}\)
=\(\dfrac{2010^2+2010-1}{2010^2+2009}+\dfrac{744-\left[377.733+1466\right]}{377.733+722}\)
=\(\dfrac{2010^2+2009}{2010^2+2009}+\dfrac{-722-377.733}{377.733+722}\)
=\(1+\left(-1\right)=0\)
Vậy P=0
\(P=\dfrac{2010\cdot2011-1}{2010^2+2009}+\dfrac{744-379\cdot733}{377\cdot733+722}=\dfrac{2010\cdot2011-2010+2009}{2010^2+2009}+\dfrac{733-379\cdot733+11}{377\cdot733+733-11}=\dfrac{2010\cdot\left(2011-1\right)+2009}{2010^2+2009}+\dfrac{733\cdot\left(1-379\right)+11}{733\cdot\left(377+1\right)-11}=\dfrac{2010^2+2009}{2010^2+2009}+\dfrac{733\cdot\left(-378\right)+11}{733\cdot378-11}=1+\left(-1\right)=0\)