\(DF=\sqrt{12}\)

1 cm³ = 1ml

\(\Rightarrow\)1ml = 1 cm³

\(92\cdot183-\dfrac{91}{91\cdot183+92}\)

\(=16836-\dfrac{91}{16745}\\ =\dfrac{281918820}{16745}-\dfrac{91}{16745}\\ =\dfrac{2819118729}{16745}\)

a) \(M\left(x\right)=P\left(x\right)+Q\left(x\right)\)

\(=x^4-5x+2x^2+1+5x+3x^2+5+\dfrac{1}{2}x^2+x\\ =x^4+\dfrac{11}{2}x^2+x+6\)

Ta có :

\(A=13\dfrac{1}{2}\\ \Leftrightarrow\dfrac{10n+3}{4n-10}=\dfrac{27}{2}\\ \Leftrightarrow\left(10n+3\right)\cdot2=\left(4n-10\right)\cdot27\\ \Leftrightarrow20n+6=108n-270\\ \Leftrightarrow6+270=108n-20n\\ \Leftrightarrow276=88n\\ \Leftrightarrow n=\dfrac{69}{22}\)

Đặt \(x=2009\)

\(A=2009^8-2010\cdot2009^7+2010\cdot2009^6-2010\cdot2009^5+...+2010\cdot2009^0\)

\(\Leftrightarrow A=x^8-\left(x+1\right)x^7+\left(x+1\right)x^6-\left(x+1\right)x^5+...+\left(x+1\right)x^0\\ \Leftrightarrow A=x^8-x^8-x^7+x^7+x^6-x^6-x^5+...-x^2-x^1+x^1+x^0\)

\(\Leftrightarrow A=x^0\\ \Leftrightarrow A=1\)

Đặt \(A=\dfrac{1}{10}-\dfrac{1}{40}-\dfrac{1}{88}-\dfrac{1}{154}-\dfrac{1}{238}-\dfrac{1}{340}\)

\(\Leftrightarrow3A=\dfrac{3}{10}-\dfrac{3}{40}-\dfrac{3}{88}-\dfrac{3}{154}-\dfrac{3}{238}-\dfrac{3}{340}\)

\(\Leftrightarrow3A=\dfrac{3}{2\cdot5}-\dfrac{3}{5\cdot8}-\dfrac{3}{8\cdot11}-\dfrac{3}{11\cdot14}-\dfrac{3}{14\cdot17}-\dfrac{3}{17\cdot20}\)

\(\Leftrightarrow3A=\left(\dfrac{1}{2}-\dfrac{1}{5}\right)-\left(\dfrac{1}{5}-\dfrac{1}{8}\right)-\left(\dfrac{1}{8}-\dfrac{1}{11}\right)-\left(\dfrac{1}{11}-\dfrac{1}{14}\right)-\left(\dfrac{1}{14}-\dfrac{1}{17}\right)-\left(\dfrac{1}{17}-\dfrac{1}{20}\right)\)

\(\Leftrightarrow3A=\dfrac{1}{2}-\dfrac{1}{5}-\dfrac{1}{5}+\dfrac{1}{8}-\dfrac{1}{8}+\dfrac{1}{11}-\dfrac{1}{11}+\dfrac{1}{14}-\dfrac{1}{14}+\dfrac{1}{17}-\dfrac{1}{17}+\dfrac{1}{20}\)

\(\Leftrightarrow3A=\dfrac{1}{2}-\dfrac{2}{5}+\dfrac{1}{20}\\ \Leftrightarrow3A=\dfrac{3}{20}\\ \Leftrightarrow A=\dfrac{1}{20}\)

\(32\left(-39\right)+16\left(-22\right)=-1248-352=-1600\)