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Bài 1 :
\(\left(\frac{1}{8}+\frac{1}{8.15}+\frac{1}{15.22}+...+\frac{1}{43.50}\right)\frac{4-3-5-7-...-49}{217}\)
\(=\frac{1}{7}\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+\frac{1}{15}-\frac{1}{22}+...+\frac{1}{43}-\frac{1}{50}\right).\frac{5-\left(1+3+5+7+...+49\right)}{217}\)
\(=\frac{1}{7}\left(1-\frac{1}{50}\right).\frac{5-\left(12.50\right)+25}{217}\)
\(=\frac{1}{7}.\frac{49}{50}.\frac{5-625}{217}\)
\(=\frac{-2}{5}\)
Bài 2 :
\(B=\frac{x^2+17}{x^2+7}=\frac{\left(x^2+7\right)+10}{x^2+7}=1+\frac{10}{x^2+7}\)
Ta có : \(x^2\ge0\). Dấu '' = '' xảy ra khi :
\(x=0\Rightarrow x^2+7\ge7\)( 2 vế dương )
\(\Rightarrow\frac{10}{x^2+7}\le\frac{10}{7}\)
\(\Rightarrow1+\frac{10}{x^2+7}\le1+\frac{10}{7}\)
\(\Rightarrow B\le\frac{17}{7}\)
Dấu '' = '' xảy ra < = > x = 0
Vậy Max \(B=\frac{17}{7}\Leftrightarrow x=0\)
A = \(\left(\frac{1}{8}+\frac{1}{8.15}+\frac{1}{15.22}+...+\frac{1}{43.50}\right)\cdot\frac{4-3-5-7-...-49}{217}\)
A = \(\frac{1}{7}.\left(\frac{7}{1.8}+\frac{7}{8.15}+\frac{7}{15.22}+...+\frac{7}{43.50}\right)\cdot\frac{4-\left(3+5+7+...+49\right)}{217}\)
A = \(\frac{1}{7}.\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+\frac{1}{15}-\frac{1}{22}+...+\frac{1}{43}-\frac{1}{50}\right)\cdot\frac{4-\left(49+3\right)\left[\left(49-3\right):2+1\right]:2}{217}\)
A = \(\frac{1}{7}\cdot\left(1-\frac{1}{50}\right)\cdot\frac{4-52.24:2}{217}\)
A = \(\frac{1}{7}\cdot\frac{49}{50}\cdot\frac{4-624}{217}\)
A = \(\frac{7}{50}\cdot\frac{-620}{217}=-\frac{2}{5}\)
a) \(\frac{1}{3}-\left(\frac{1}{2}+\frac{1}{8}\right)\)
= \(\frac{1}{3}-\left(\frac{4}{8}+\frac{1}{8}\right)\)
= \(\frac{1}{3}-\frac{5}{8}\)
= \(\frac{8}{24}-\frac{15}{24}\)
= \(\frac{-7}{24}\)
b) \(\frac{1}{2}-\frac{1}{4}+\frac{1}{13}+\frac{1}{8}\)
= \(\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}\right)\)+ \(\frac{1}{13}\)
= \(\left(\frac{4}{8}-\frac{2}{8}+\frac{1}{8}\right)+\frac{1}{13}\)
= \(\frac{1}{8}+\frac{1}{13}\)
= \(\frac{13}{104}+\frac{8}{104}\)
= \(\frac{23}{104}\)
c) \(13\frac{2}{7}:\left(\frac{-8}{9}\right)+2\frac{5}{7}:\left(\frac{-8}{9}\right)\)
= \(\left(13\frac{2}{7}+2\frac{5}{7}\right):\left(\frac{-8}{9}\right)\)
= \(16:\left(\frac{-8}{9}\right)\)
= -18
a, \(-\frac{2}{5}+\frac{5}{3}\left(\frac{3}{2}-\frac{4}{15}x\right)=\frac{7}{6}\)
\(\frac{5}{3}\left(\frac{3}{2}-\frac{4}{15}x\right)=\frac{47}{30}\)
\(\frac{3}{2}-\frac{4}{15}x=\frac{47}{50}\)
\(\frac{4}{15}x=\frac{14}{25}\)
\(x=\frac{21}{10}\)