Tính \(\left(\frac{5}{7}\right)^9.\left(\frac{7}{5}\right)^8-\sqrt{\frac{1}{9}}\)
Tìm x, y, z: \(\frac{2x+1}{-15}=\frac{2}{3}\)
\(\sqrt{x}-3=5\)với x ≥ 0
2x = 3y = 5z & x – 3y + 5z = -75
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\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)
\(=3-\left(-1\right)\)
\(=4\)
b) \(=\left(\frac{1}{4}+\frac{25}{2}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3}{8}-\frac{1}{12}\right)\right)\)
\(=\left(\frac{4}{16}+\frac{200}{16}-\frac{5}{16}\right):\left(12-\frac{7}{12}:\left(\frac{3.3}{2.3.4}-\frac{2}{2.3.4}\right)\right)\)
\(=\left(\frac{199}{16}\right):\left(12-\frac{7}{12}:\left(\frac{9}{24}-\frac{2}{24}\right)\right)\)
\(=\frac{199}{16}:\left(12-\frac{7}{12}.\frac{24}{7}\right)\)
\(=\frac{199}{16}:\left(12-2\right)\)
\(=\frac{199}{16}:10\)
\(=\frac{199}{160}\)
c) \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)
\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)
\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)
\(A=\left(-\frac{5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(A=-\frac{7}{33}+-2\)
\(A=-\frac{73}{33}\)
[ A] = -2
\(\left(\frac{5}{7}\right)^9\).\(\left(\frac{7}{5}\right)^8\)-\(\sqrt{\frac{1}{9}}\)= \(\frac{5^9.7^8}{7^9.5^8}-\frac{1}{3}=\frac{5}{7}-\frac{1}{3}=\frac{8}{21}\)
\(\frac{2x+1}{-15}=\frac{2}{3}\Rightarrow2x+1=-10\Rightarrow2x=-11\Rightarrow x=\frac{-11}{2}\)
\(\sqrt{x}-3=5\Rightarrow\sqrt{x}=8\Rightarrow x=64\)(vì \(x\ge0\))
2x=3y=5z và x-3y+5z=-75
ta có \(\frac{x}{\frac{1}{2}}=\frac{3y}{1}=\frac{5z}{1}=\frac{x-3y+5z}{\frac{1}{2}+1+1}=\frac{-75}{\frac{5}{2}}=-30\)
suy ra x=-15; y=-10; z=-6