a) \(\dfrac{4}{5}< \dfrac{5}{a}< \dfrac{10}{7}\) \(\left(a\inℤ\right)\)

\(\Leftrightarrow\dfrac{7}{10}< \dfrac{a}{5}< \dfrac{5}{4}\)

\(\Leftrightarrow\dfrac{7.5}{10}< a< \dfrac{5}{4}.5\)

\(\Leftrightarrow\dfrac{7}{2}< a< \dfrac{25}{4}\)

\(\Leftrightarrow a\in\left\{4;5;6\right\}\)

b) \(\dfrac{2}{5}< \dfrac{a-1}{10}< \dfrac{8}{15}\)

\(\Leftrightarrow\dfrac{2.10}{5}< a-1< \dfrac{8.10}{15}\)

\(\Leftrightarrow4< a-1< \dfrac{16}{3}\)

\(\Leftrightarrow5< a< \dfrac{19}{3}\)

\(\Leftrightarrow a\in\left\{6\right\}\)

c) \(\dfrac{12}{7}< \dfrac{4}{a}< \dfrac{8}{3}\)

\(\Leftrightarrow\dfrac{3}{8}< \dfrac{a}{4}< \dfrac{7}{12}\)

\(\Leftrightarrow\dfrac{3.4}{8}< a< \dfrac{7.4}{12}\)

\(\Leftrightarrow\dfrac{3}{2}< a< \dfrac{7}{3}\)

\(\Leftrightarrow a\in\left\{2\right\}\)

d) \(5< a^2-15< 16\)

\(\Leftrightarrow10< a^2< 31\)

\(\Leftrightarrow\sqrt[]{10}< a< \sqrt[]{31}\)

\(\Leftrightarrow a\in\left\{4;5\right\}\)

a)\(a+a+a+\dfrac{1}{2}x2\dfrac{2}{5}+a+\dfrac{14}{5}+a=134\)

\(5xa+\dfrac{1}{2}x\dfrac{12}{5}+\dfrac{14}{5}=134\)

\(5xa+\dfrac{12}{10}+\dfrac{14}{5}=134\)

\(5xa+\dfrac{6}{5}+\dfrac{14}{5}=134\)

\(5xa+4=134\)

\(5xa=134-4=130\)

\(a=130:5=26\)

b)\(5\dfrac{4}{10}-yx\dfrac{3}{4}=\dfrac{2}{3}\)

\(\dfrac{54}{10}-yx\dfrac{3}{4}=\dfrac{2}{3}\)

\(yx\dfrac{3}{4}=\dfrac{54}{10}-\dfrac{2}{3}\)

\(yx\dfrac{3}{4}=\dfrac{71}{15}\)

\(y=\dfrac{71}{15}:\dfrac{3}{4}\)

\(y=\dfrac{284}{45}\)

đề bài khó hỉu quá

1: \(=\left(a-3\right)\cdot\dfrac{\left|b\right|}{a-3}=\left|b\right|\)

2: \(\dfrac{1}{3+a}\cdot\sqrt{\dfrac{a^2+6a+9}{b^2}}\)

\(=\dfrac{1}{a+3}\cdot\dfrac{\left|a+3\right|}{b}=\pm\dfrac{1}{b}\)

3: \(=\left|a+1\right|-\dfrac{3a}{a-2}\cdot\dfrac{\left|a-2\right|}{3}\)

\(=\left|a+1\right|-a\)

4: \(=-6\sqrt{3}+6+28+6\sqrt{3}=34\)

 \(a+b=10\) và \(ab=4\)

1. Có: \(A=a^2+b^2=\left(a+b\right)^2-2ab=10^2-2.4=92\)

2. \(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)=10^3-3.4.10=880\)

3. \(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=92^2-2.4^2=8432\)

4. \(a^5+b^5=\left(a^2+b^2\right)\left(a^3+b^3\right)-a^2b^2\left(a+b\right)=92.880-4^2.10=80800\)

\(S=a^1+a^2+a^3+...+a^{13}=7\)

\(\Leftrightarrow\)\(\left(a^1+a^2+a^3\right)+\left(a^4+a^5+a^6+a^7+a^8+a^9+a^{10}+a^{11}+a^{12}\right)\)\(+a^{13}=7\)

\(\Leftrightarrow\)\(5+5+a^{13}=7\)

\(\Leftrightarrow\)\(a^{13}=7-5-5=-3\)