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Ta thấy A gấp 12+22+....+102 4 lần nên Tổng A gấp 4 lần nó
=> A=385.4=1540
Đặt S = \(1^2+2^2+3^2+\cdots+\) \(10^2\)
Ta có: \(2^2=(2\cdot1)^2=\) \(4\cdot1^2\)
\(4^2=(2\cdot2)^2\) \(=4\cdot2^2\)
...
\(20^2=(2\cdot10)^2=4\cdot10^2\)
=> \(A=4\cdot1^2+4\cdot2^2+4\cdot3^2+\cdots+4\cdot10^2\)
\(A=4\cdot\left(1^2+2^2+3^2+\cdots+10^2\right)=4S\)
\(\Rightarrow4S=4\cdot385\)
\(4S=1540\)
\(\Rightarrow A=1540\)
\(\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\\\Rightarrow\left[\left(2^2.6^2\right)+\left(2^2.7^2\right)....+\left(2^2.10^2\right)\right]-\left(1^2+3^2+...+9^2\right)\\ \Rightarrow2^2.\left(6^2+7^2....+.10^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\\ \Rightarrow4.330-165=1155\)
\(=\frac{16}{5}.\frac{15}{16}-\left(\frac{3}{4}+\frac{2}{7}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{21}{28}+\frac{8}{28}\right):\left(\frac{-29}{28}\right)\)
\(=3-\left(\frac{29}{28}\right).\left(\frac{-28}{29}\right)\)
\(=3-\left(-1\right)\)
\(=4\)
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) \(\left(\frac{-3}{5}+\frac{5}{11}\right):\frac{-3}{7}+\left(\frac{-2}{5}+\frac{6}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-33}{55}+\frac{25}{55}\right):\frac{-3}{7}+\left(\frac{4}{5}\right):\frac{-3}{7}\)
\(\left(\frac{-8}{55}\right).\frac{-7}{3}+\frac{4}{5}.\frac{-7}{3}\)
\(\frac{-7}{3}\left(\frac{-8}{55}+\frac{4}{5}\right)\)
\(\frac{-7}{3}.\frac{36}{55}=\frac{-84}{55}\)
\(A=\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\)
\(A=\left(12^2-1^2\right)+\left(14^2-3^2\right)+\left(16^2-5^2\right)+\left(18^2-7^2\right)+\left(20^2-9^2\right)\)\(A=\left(12+1\right)\left(12-1\right)+\left(14+3\right)\left(14-3\right)+\left(16-5\right)\left(16+5\right)+\left(18-7\right)\left(18+7\right)+\left(20-9\right)\left(20+9\right)\)
\(A=11.13+11.17+11.21+11.25+11.29\)
\(A=11.\left(13+17+21+25+29\right)\)
\(A=11.\left[\left(13+17\right)+\left(21+29\right)+25\right]\)
\(A=11.\left(30+50+25\right)\)
\(A=11.105=1155\)