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\(1,\\ x+\dfrac{1}{2}=-\dfrac{5}{3}\\ x=-\dfrac{5}{3}-\dfrac{1}{2}\\ x=-\dfrac{13}{6}\\ Vậyx=-\dfrac{13}{6}\)
\(2,\\ \dfrac{1}{3}-x=\dfrac{3}{5}\\ x=\dfrac{1}{3}-\dfrac{3}{5}\\ x=-\dfrac{4}{15}\\ Vậyx=-\dfrac{4}{15}\)
\(3,\\ 3-4+x=\dfrac{7}{2}\\ -1+x=\dfrac{7}{2}\\ x=\dfrac{7}{2}+1\\ x=\dfrac{9}{2}\\ Vậyx=\dfrac{9}{2}\)
\(4,\\ x-\dfrac{4}{3}=-\dfrac{7}{9}\\ x=-\dfrac{7}{9}+\dfrac{4}{3}\\ x=\dfrac{15}{27}\\ Vậyx=\dfrac{15}{27}\)
\(5,\\ x-\left(-\dfrac{7}{3}\right)=\dfrac{5}{6}\\ x=\dfrac{5}{6}-\dfrac{7}{3}\\ x=-\dfrac{27}{18}\\ Vậyx=-\dfrac{27}{18}\)
\(6,\\ x-\dfrac{1}{5}=\dfrac{9}{10}\\ x=\dfrac{9}{10}+\dfrac{1}{5}\\ x=\dfrac{11}{10}\\ Vậyx=\dfrac{11}{10}\)
\(7,\\ x+\dfrac{5}{12}=\dfrac{3}{8}\\ x=\dfrac{3}{8}-\dfrac{5}{12}\\ x=-\dfrac{1}{24}\\ Vậyx=-\dfrac{1}{24}\)
\(8,\\ x+\dfrac{5}{4}=\dfrac{7}{6}\\ x=\dfrac{7}{6}-\dfrac{5}{4}\\ x=-\dfrac{9}{24}\\ Vậyx=-\dfrac{9}{24}\)
\(9,\\ x-\dfrac{2}{7}=\dfrac{1}{35}\\ x=\dfrac{1}{35}+\dfrac{2}{7}\\ x=\dfrac{11}{35}\\ Vậyx=\dfrac{11}{35}\\ 10,\\ x-\dfrac{1}{5}=-\dfrac{7}{10}\\ x=-\dfrac{7}{10}+\dfrac{1}{5}\\ x=-\dfrac{1}{2}\\ Vậyx=-\dfrac{1}{2}\)
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\(\text{Ta có:}2;6;10;...;8010\text{ đều chia 4 dư 2}\)
\(\Rightarrow X\equiv2^2+3^2+4^2+....+2004^2\left(mod\text{ }10\right)\)
\(\text{ mà:}1^2+2^2+3^2+....+2004^2=\frac{2004.2005.4009}{6}=333.2005.4009\)
\(\Rightarrow X\equiv333.2005.4009-1\left(\text{mod 10}\right)\equiv3.5.9-1\equiv4\left(\text{mod 10}\right)\)
Vậy X có chữ số tận cùng là 4
\(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2^{10}-1}\)
\(< 1+\frac{1}{2}+\frac{1}{2}+\left(\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{2^2}\right)+..........\left(\frac{1}{2^9}+\frac{1}{2^9}+....+\frac{1}{2^9}\left(\text{512 số hạng }\frac{1}{2^9}\right)\right)\)
\(=1+1+1+1+1+1+1+1+1+1\)
\(=10\left(\text{điều phải chứng minh}\right)\)
\(\text{bài 2 câu b tương tự câu a}\)
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2. \(7\left(-3\right)-5\left(3-x\right)=11-5\)
\(\Leftrightarrow-21-5\left(3-x\right)=6\)
\(\Leftrightarrow-5\left(3-x\right)=27\)
\(\Leftrightarrow3-x=-\frac{27}{5}\)
\(\Leftrightarrow x=-\frac{42}{5}\)
Vậy \(x=-\frac{42}{5}\)
Khó quá :((
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\(x\div4\frac{1}{3}=-2,5\)
\(\Leftrightarrow x\div\frac{13}{3}=\frac{-5}{2}\)
\(\Leftrightarrow x=\frac{-5}{2}.\frac{13}{3}\)
\(\Leftrightarrow x=\frac{-65}{6}\)
\(x\div\frac{-3}{5}=\frac{-10}{21}\)
\(\Leftrightarrow x=\frac{-10}{21}.\frac{-3}{5}\)
\(\Leftrightarrow x=\frac{30}{105}\)
\(\Leftrightarrow x=\frac{2}{7}\)
\(\frac{2}{3}x-\frac{1}{2}=\frac{1}{10}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{1}{10}+\frac{1}{2}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{6}{10}\)
\(\Leftrightarrow x=\frac{6}{10}\div\frac{2}{3}\)
\(\Leftrightarrow x=\frac{18}{20}\)
\(\Leftrightarrow x=\frac{9}{10}\)
\(\frac{1}{2}x+\frac{1}{2}=\frac{5}{2}\)
\(\Leftrightarrow\frac{1}{2}\left(x+1\right)=\frac{5}{2}\)
\(\Leftrightarrow\left(x+1\right)=\frac{5}{2}\div\frac{1}{2}\)
\(\Leftrightarrow\left(x+1\right)=5\)
\(\Leftrightarrow x=5-1\)
\(\Leftrightarrow x=4\)
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\(\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}\)
Vậy x = -4 . -10 : 8 = 5
=> Y = -10 . 7 : 5 = 14
Câu 2 ( CHỊU) BÓ TAY
\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}\)
\(\Rightarrow A< \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\)
\(\Rightarrow A< \frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\) ( 9 số hạng \(\frac{1}{10}\))
\(\Rightarrow A< \frac{9}{10}< 1\)
Vậy \(A< 1\left(đpcm\right)\)
22 + 1 + 4. 2x = 10 . 210
5 + 22.2x = 10. 210
5 + 2x+2 = 10. 210
nếu x ≤ 0 ⇔ 5 + 2x+2 ≤ 5 + 1 = 6 < 10.210 (loại) (1)
nếu x > 0 ta có 2x+2 là số chẵn ⇔ 5 + 2x+2 là số lẻ
10.210 = \(\overline{....0}\) là số chẵn
vậy nếu x > 0 ⇔ 5 + 2x+2 # 10 . 210 (loại) (2)
kết hợp (1) và (2) ta có pt vô nghiệm