tính
\(\dfrac{-15}{16}\).\(\dfrac{8}{-25}\)
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NH
8
1 tháng 5 2023
a) Ta có \(A=\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdot...\cdot\dfrac{2499}{2500}\)
\(=\dfrac{2\cdot4}{3\cdot3}\cdot\dfrac{3\cdot5}{4\cdot4}\cdot\dfrac{4\cdot6}{5\cdot5}\cdot...\cdot\dfrac{49\cdot51}{50\cdot50}\)
\(=\dfrac{2\cdot4\cdot3\cdot5\cdot4\cdot6\cdot...\cdot49\cdot51}{3\cdot3\cdot4\cdot4\cdot5\cdot5\cdot...\cdot50\cdot50}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot49}{3\cdot4\cdot5\cdot...\cdot50}\cdot\dfrac{4\cdot5\cdot6\cdot...\cdot51}{3\cdot4\cdot5\cdot...\cdot50}\)
= \(\dfrac{2}{50}\cdot17=\dfrac{17}{25}\)
b) Vì n nguyên nên 3n - 1 nguyên
Để phân số \(\dfrac{12}{3n-1}\) có giá trị nguyên thì 12 ⋮ ( 3n - 1 ) hay ( 3n - 1 ) ϵ Ư( 12 )
Ư( 12 ) = { \(\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\) }
Lập bảng giá trị
| 3n - 1 | 1 | -1 | 2 | -2 | 3 | -3 | 4 | -4 | 6 | -6 | 12 | -12 |
| n | \(\dfrac{2}{3}\) | 0 | 1 | \(\dfrac{-1}{3}\) | \(\dfrac{3}{4}\) | \(\dfrac{-2}{3}\) | \(\dfrac{5}{3}\) | -1 | \(\dfrac{7}{3}\) | \(\dfrac{-5}{3}\) | \(\dfrac{13}{3}\) | \(\dfrac{-11}{3}\) |
Vì n nguyên nên n ϵ { 0; 1; -1 }
Vậy n ϵ { 0; 1; -1 } để phân số \(\dfrac{12}{3n-1}\) có giá trị nguyên
21 tháng 6 2021
a) \(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{120}{121}.\dfrac{143}{144}\)
= \(\dfrac{1.3.2.4.3.5.4.6....10.12.11.13}{2^2.3^2.4^2.5^2...11^2.12^2}\)
= \(\dfrac{1.2.12.13}{2^2.12^2}=\dfrac{13}{2.12}=\dfrac{13}{24}\)
b) \(B=\dfrac{5}{9}.\dfrac{21}{25}.\dfrac{45}{49}.\dfrac{77}{81}....\dfrac{357}{361}.\dfrac{437}{441}\)
= \(\dfrac{1.5.3.7.5.9.7.11.....17.21.19.23}{3^2.5^2.7^2....19^2.21^2}=\dfrac{1.3.21.23}{3^2.21^2}\)
= \(\dfrac{23}{3.21}=\dfrac{23}{63}\)
MN
9 tháng 5 2021
\(a.\)
\(\dfrac{3}{16}:\dfrac{?}{8}=\dfrac{3}{4}\)
\(\Leftrightarrow\dfrac{3}{16}\cdot\dfrac{8}{?}=\dfrac{3}{4}\)
\(\Leftrightarrow\dfrac{3}{2?}=\dfrac{3}{4}\)
\(\Leftrightarrow?=2\)
\(b.\)
\(\dfrac{1}{25}:-\dfrac{3}{?}=-\dfrac{1}{15}\)
\(\Leftrightarrow\dfrac{1}{25}\cdot\dfrac{-?}{3}=-\dfrac{1}{15}\)
\(\Leftrightarrow\dfrac{-?}{75}=-\dfrac{1}{15}\)
\(\Leftrightarrow?=\dfrac{75}{15}=5\)
\(c.\)
\(\dfrac{?}{12}:-\dfrac{4}{9}=-\dfrac{3}{16}\)
\(\Leftrightarrow\dfrac{?}{12}\cdot\dfrac{-9}{4}=-\dfrac{3}{16}\)
\(\Leftrightarrow\dfrac{-3?}{16}=-\dfrac{3}{16}\)
\(\Leftrightarrow?=1\)
9 tháng 5 2021
Mk gọi ? = x nha
a) \(\dfrac{3}{16}:\dfrac{x}{8}=\dfrac{3}{4}\)
\(\dfrac{x}{8}=\dfrac{3}{16}:\dfrac{3}{4}\)
\(\dfrac{x}{8}=\dfrac{1}{4}\)
⇒\(x=\dfrac{1.8}{4}=2\)
b) \(\dfrac{1}{25}:\dfrac{-3}{x}=\dfrac{-1}{15}\)
\(\dfrac{-3}{x}=\dfrac{1}{25}:\dfrac{-1}{15}\)
\(\dfrac{-3}{x}=\dfrac{-3}{5}\)
⇒x=5
c) \(\dfrac{x}{12}:\dfrac{-4}{9}=\dfrac{-3}{16}\)
\(\dfrac{x}{12}=\dfrac{-3}{16}.\dfrac{-4}{9}\)
\(\dfrac{x}{12}=\dfrac{1}{12}\)
⇒x=1
25 tháng 5 2022
Ta có: \(2x^3-1=15\Leftrightarrow x^3=8\Rightarrow x=2\)
\(\Rightarrow\dfrac{18}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\Rightarrow\left\{{}\begin{matrix}\dfrac{y-25}{16}=2\Rightarrow y=57\\\dfrac{z+9}{25}=2\Rightarrow z=41\end{matrix}\right.\)
Vậy \(B=x+y+z=2+57+41=100\)
28 tháng 10 2021
\(=\dfrac{2^{30}\cdot3^{16}\cdot5^{16}}{2^{30}\cdot3^{15}\cdot5^{16}}=3\)
ta rút gọn là xong