(a+1)+(a+2)+(a+3)+(a+4)+(a+5)+...(a+10)
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Tìm số nguyên a
a)4/5<5/a<10/7 b)2/5<a-1/10<8/15(a-1 là tử, 10 là mẫu)
c)12/7<4/a<8/3. d)5<a^2-15<16
1
14 tháng 9 2023
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) \(5< a^2-15< 16\)
\(\Leftrightarrow10< a^2< 31\)
\(\Leftrightarrow\sqrt[]{10}< a< \sqrt[]{31}\)
\(\Leftrightarrow a\in\left\{4;5\right\}\)
12 tháng 8 2023
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)\(5\dfrac{4}{10}-yx\dfrac{3}{4}=\dfrac{2}{3}\)
\(\dfrac{54}{10}-yx\dfrac{3}{4}=\dfrac{2}{3}\)
\(yx\dfrac{3}{4}=\dfrac{54}{10}-\dfrac{2}{3}\)
\(yx\dfrac{3}{4}=\dfrac{71}{15}\)
\(y=\dfrac{71}{15}:\dfrac{3}{4}\)
\(y=\dfrac{284}{45}\)
5 tháng 8 2022
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: \(=-6\sqrt{3}+6+28+6\sqrt{3}=34\)
NG
1
30 tháng 9 2019
\(a+b=10\) 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. \(a^5+b^5=\left(a^2+b^2\right)\left(a^3+b^3\right)-a^2b^2\left(a+b\right)=92.880-4^2.10=80800\)
a + 1 + a + 2 + a + 3 + a +4 +...+ a + 10
a x 10 +( 1+2+3+4+...+10)
a x 10 + 55 = ......