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=\(\frac{1}{1975}.\frac{2}{1945}-\frac{1}{1975}-\frac{1}{1975}-\frac{1}{1975}.\frac{2}{1975}-\frac{1974}{1975}.\frac{1946}{1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-1-1-\frac{2}{1975}\right)-\frac{1974.1946}{1975.1945}-\frac{3}{1975.1945}\)
=\(\frac{1}{1975}.\left(\frac{2}{1945}-\frac{2}{1975}-2\right)-\frac{1974.1946-3}{1975.1945}\)
\(\left|x-\frac{5}{7}\right|\ge0\Rightarrow\left|x-\frac{5}{7}\right|+\frac{2}{3}\ge\frac{2}{3}\Rightarrow A_{min}=\frac{2}{3}.\text{Dâu "=" xay ra}\Leftrightarrow x=\frac{5}{7}\)
\(\left|5-x\right|\ge0\Rightarrow\left|5-x\right|-8,5\ge-8,5\Rightarrow B_{min}=-8,5.\text{ Dâu "=" xay ra}\Leftrightarrow x=5\)
Vì \(\left|x+\frac{19}{5}\right|\ge0\) với \(\forall x\)
\(\left|y+\frac{1890}{1975}\right|\ge0\) với \(\forall y\)
\(\left|z-2004\right|\ge0\)với \(\forall z\)
\(\Rightarrow\left|x+\frac{19}{5}\right|+\left|y+\frac{1890}{1975}\right|+\left|z-2004\right|\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}\left|x+\frac{19}{5}\right|=0\\\left|y+\frac{1890}{1975}\right|=0\\\left|z-2004\right|=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-\frac{19}{5}\\y=-\frac{1890}{1975}\\z=2004\end{cases}}\)
\(\left(1+\frac{1}{1}\right).\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).\left(1+\frac{1}{5}\right).\left(1+\frac{1}{6}\right)\)
\(=2.\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}.\frac{7}{6}\)
\(=\frac{2.3.4.5.6.7}{2.3.4.5.6}=7\)