\(\left(10^9-5^7\right)⋮59\)
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Tính hợp lý :
\(\left(5-\frac{43}{10}\right)-\left(\frac{42}{19}-\left(\frac{7}{2}-\frac{59}{10}\right)\right)+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(\left(5-\frac{43}{10}\right)-\left(\frac{42}{19}-\left(\frac{7}{2}-\frac{59}{10}\right)\right)+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}-\left(\frac{42}{19}-\frac{7}{2}+\frac{59}{10}\right)+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}-\frac{42}{19}+\frac{7}{2}-\frac{59}{10}+\frac{42}{19}+\frac{59}{10}+\frac{4}{5}\)
\(=5-\frac{43}{10}+\frac{7}{2}+\frac{4}{5}\)
\(=5+\frac{35}{10}+\frac{8}{10}-\frac{43}{10}=5\)
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Câu 1: Thực hiện phép tính
a, \(\dfrac{7}{9}-\dfrac{16}{9}\)
b, \(\dfrac{2}{-15}+\dfrac{7}{10}\)
c, \(\left(4\dfrac{2}{3}-4\dfrac{3}{4}\right):\dfrac{-5}{12}-\dfrac{4}{5}\)
d, \(\dfrac{-141}{157}.\dfrac{23}{59}-\dfrac{141}{157}.\dfrac{36}{59}+\dfrac{16}{-157}\)
a. 7/9 - 16/9 = -9/9 = -1
b. 2/-15 + 7/10 = 17/30
c. (4 2/3 - 4 3/4) : -5/12 - 4/5
= (14/3 - 19/4) : (-5/12) - 4/5
= -1/12 : (-5/12) - 4/5
= 1/5 - 4/5
= -3/5
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Ffrac{left(frac{53}{4}-frac{59}{27}-frac{65}{6}right).left(230+frac{1}{25}right)+frac{187}{4}}{left(frac{25}{7}+frac{10}{3}right):left(frac{37}{3}-frac{100}{7}right)} Gfrac{left(frac{-5}{7}-frac{7}{9}+frac{9}{11}-frac{11}{13}right).left(3-frac{3}{4}right)}{left(frac{10}{21}+frac{14}{27}-frac{6}{11}+frac{22}{39}right):left(2+frac{2}{3}right)}làm giúp mk nhanh với mk tặng sao nhen
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\(F=\frac{\left(\frac{53}{4}-\frac{59}{27}-\frac{65}{6}\right).\left(230+\frac{1}{25}\right)+\frac{187}{4}}{\left(\frac{25}{7}+\frac{10}{3}\right):\left(\frac{37}{3}-\frac{100}{7}\right)}\) \(G=\frac{\left(\frac{-5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}\right).\left(3-\frac{3}{4}\right)}{\left(\frac{10}{21}+\frac{14}{27}-\frac{6}{11}+\frac{22}{39}\right):\left(2+\frac{2}{3}\right)}\)
làm giúp mk nhanh với mk tặng sao nhen
làm giúp mk đi mà chiều mk phải nộp rồi
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\(tinh\left(2\frac{1}{5}+3\frac{7}{10}\right):59+\frac{9}{10}\)
\(\frac{5^2}{1.6}+\frac{5^2}{6.1}+...+\frac{5^2}{2016.2021}\)
Chung minh rang \(\left(10^6-5^7\right)\)chia het cho 59
\(10^6-5^7\)
= \(\left(2.5\right)^6-5^7\)
= \(2^6.5^6-5^7\)
= \(5^6.\left(2^6-5\right)\)
= \(5^6.59\) \(⋮\) \(59\)
\(\Rightarrow\left(10^6-5^7\right)⋮59\)
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Chứng minh rằng
\(\left(10^6-5^7\right)\) chia hết cho 59
Ta có 10\(^6\) - 5\(^7\) = 2\(^6\) . 5\(^6\) - 5\(^7\)
= 5\(^6\) . (2\(^6\) - 5)
= 5\(^6\) . (6\(^4\) - 5)
= 5\(^6\) . 5\(^9\) chia hết cho 59
Vậy 10\(^6\) - 5\(^7\) chia hết cho 59
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rút gọn :
a ) \(\sqrt{2}.\sqrt{7-3\sqrt{5}}\)
b) \(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}\)
c) \(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
d) \(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(\Leftrightarrow\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right).\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)
\(\Leftrightarrow\sqrt{7}\left(\sqrt{7}+\sqrt{2}\right).\left(\sqrt{7}-\sqrt{2}\right)\)
\(\Leftrightarrow\sqrt{7}\left(7-2\right)\)
\(\Leftrightarrow5\sqrt{7}\)
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\(\sqrt{2}.\sqrt{7-3\sqrt{5}}\)
\(\Leftrightarrow\sqrt{2\left(7-3\sqrt{5}\right)}\)
\(\Leftrightarrow\sqrt{14-6\sqrt{5}}\)
\(\Leftrightarrow\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(\Leftrightarrow3-\sqrt{5}\)
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a)\(\sqrt{2}.\sqrt{7-3\sqrt{5}}=\sqrt{14-2.3\sqrt{5}}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
b)\(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}=\sqrt{\dfrac{9}{25}+2.\dfrac{3}{5}.\sqrt{2}+2}=\sqrt{\left(\dfrac{3}{5}+\sqrt{2}\right)^2}=\dfrac{3}{5}+\sqrt{2}\)
c)\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
\(=2\sqrt{2}.\left(\sqrt{5}-1\right).\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\)
\(=2\sqrt{2}\left(\sqrt{5}-1\right)\sqrt{3+\sqrt{5}}\)
\(=2\left(\sqrt{5}-1\right)\sqrt{6+2\sqrt{5}}\)
\(=2\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)\)
\(=2\left(5-1\right)=2.4=8\)
d)\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
\(=\left(7+\sqrt{14}\right).\sqrt{\left(\sqrt{7}-\sqrt{2}\right)^2}\)
\(=\sqrt{7}.\left(\sqrt{7}+\sqrt{2}\right).\left(\sqrt{7}-\sqrt{2}\right)\)
\(=\sqrt{7}.\left(7-2\right)=5\sqrt{7}\)
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\(A=\left\{\frac{1999}{2011}-\frac{2011}{1999}\right\}-\left\{\frac{-12}{1999}-\frac{12}{2011}\right\}\)
\(B=\frac{2}{5}+\left(\frac{3}{11}+\frac{-2}{5}\right)\)
\(C=\frac{-5}{7}.\frac{4}{13}+\frac{-5}{7}.\frac{9}{13}+\frac{-2}{7}\)
\(D=\frac{-9}{10}.\frac{5}{14}+\frac{1}{10}.\left(\frac{-9}{2}\right)+\frac{1}{7}.\left(\frac{-9}{10}\right)\)
\(-\frac{3}{7}+\frac{5}{9}:\frac{-35}{18}\left(-\frac{34}{59}\right)^0+-\left(1\right)^{2017}\)
Đề dễ nha
ko giải được thỉ mik giải
có giải đấy
người nhanh nhất và chính xác
thưởng 3
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\(\frac{-3}{7}+\frac{5}{9}:\frac{-35}{18}\cdot\left(\frac{-34}{59}\right)^0+\left(-1\right)^{2017}\)
\(=\frac{-3}{7}+\frac{5}{9}\cdot\frac{-18}{35}\cdot1+\left(-1\right)\)
\(=\frac{-3}{7}+\frac{-2}{7}+\left(-1\right)\)
\(=\frac{-5}{7}+\left(-1\right)\)
\(=\frac{-5}{7}+\frac{-7}{7}=\frac{-12}{7}\)
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\(\frac{-3}{7}+\frac{5}{9}:\left(\frac{-35}{18}\right).\left(\frac{-34}{59}\right)^0+-\left(1\right)^{2017}\)
\(=\frac{-3}{7}+\frac{5}{9}:\left(\frac{-35}{18}\right)-1\)
\(=\frac{-3}{7}+\frac{5}{9}.\left(\frac{-18}{35}\right)-1\)
\(=\frac{-3}{7}+\left(\frac{-2}{7}\right)-1\)
\(=\frac{-3-2}{7}-1=\frac{-5}{7}-1=\frac{-12}{7}\)
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