Tìm a,b \(\in Z\) biết \(\frac{a}{9}+\frac{3}{b}=\frac{1}{18}\)
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b)
\(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(21.\frac{1}{2}\right)\)
\(\Rightarrow\frac{41}{9}:\frac{41}{18}-7< x< \left(\frac{16}{5}:\frac{16}{5}+\frac{9}{2}.\frac{76}{45}\right):\frac{21}{2}\)
\(\Rightarrow2-7< x< \left(1+\frac{38}{5}\right):\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{43}{5}:\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{86}{105}\)
Vì \(x\in Z\left(gt\right)\)
\(\Rightarrow x\in\left\{-4;-3;-2;-1;0\right\}.\)
Vậy \(x\in\left\{-4;-3;-2;-1;0\right\}.\)
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Câu hỏi của Lê Nguyễn Minh Hằng - Toán lớp 7 | Học trực ... - Hoc24
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a)\(\frac{2a+8}{5}-\frac{a}{5}=\frac{a+8}{5}\)
Để \(\frac{2a+8}{5}-\frac{a}{5}\in Z\) thì: \(a+8\in B\left(5\right)\)
b)\(\frac{2a+9}{a+3}-\frac{5a+17}{a+3}-\frac{3a}{a+3}=\frac{2a+9-5a-17-3a}{a+3}=\frac{-6a-8}{a+3}\)
\(=\frac{-6a-18}{a+3}+\frac{10}{a+3}=\frac{-6.\left(a+3\right)}{a+3}+\frac{10}{a+3}=-6+\frac{10}{a+3}\)
Để: \(\frac{2a+9}{a+3}-\frac{5a+17}{a+3}-\frac{3a}{a+3}\in Z\) thì:
\(a+3\inƯ\left(10\right)=\left\{1;-1;2;-2;5;-5;10;-10\right\}\)
=>a = -2;-4;-1;-5;2;-8;7;-13
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Ta có: 1/2 - (1/3 + 1/4) = 1/2 - 7/12 = -1/12 ;
1/48 - (1/16 - 1/6) = 1/48 + 5/48 = 1/8
Vì \(-\frac{1}{12}< x< \frac{1}{8}\) nên x = 0
b) \(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(-21\frac{2}{3}\right)\)Ta có :
\(4\frac{5}{9}:2\frac{5}{18}-7=2-7=-5\)
\(\left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(-21\frac{2}{3}\right)=\left(1+\frac{38}{5}\right):\left(-21\frac{2}{3}\right)=\frac{43}{5}:\frac{-65}{3}=-\frac{129}{325}\)
Vì \(-5< x< -\frac{129}{325}\) nên \(x\in\left\{-4;-3;-2;-1\right\}\)
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a/ \(\frac{x-1}{9}=\frac{8}{3}\)
\(\Leftrightarrow3\left(x-1\right)=72\)
\(\Leftrightarrow x-1=24\)
\(\Leftrightarrow x=25\)
Vậy ..
b/ \(\frac{-x}{4}=\frac{-9}{x}\)
\(\Leftrightarrow x^2=36\)
\(\Leftrightarrow x^2=6^2=\left(-6\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}x=6\\x=-6\end{cases}}\)
Vậy ..
c/ \(\frac{x}{4}=\frac{18}{x+1}\)
\(\Leftrightarrow x\left(x+1\right)=72\)
\(\Leftrightarrow x\left(x+1\right)=8.9\)
\(\Leftrightarrow x=8\)
Vậy ..
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a)Ta có: 1/2-(1/3+1/4)= -1/12
1/48-(1/16-1/6)=1/8
suy ra: -1/12<x<1/8
<=> -2/24<x<3/24
=>x thuộc:(-1/24 ;0 ;1/24 ;2/24 ;3/24)
\(\frac{a}{9}+\frac{3}{b}=\frac{1}{18}\)
\(\frac{3}{b}=\frac{1-2a}{18}\)
\(\Leftrightarrow\left(1-2a\right)b=3.18\)
\(\left(1-2a\right)b=48\)
\(\Rightarrow1-2a;b\in\text{Ư}_{\left(48\right)}\)
\(\text{mà 2a là số chẵn }\Rightarrow1-2a\text{là số lẻ }\)
Tự làm típ nhó, đag bận òi
Tớ đã trờ lại và mang lời giải tới với cậu nè:
\(\frac{a}{9}-\frac{3}{b}=\frac{1}{18}\)
\(\frac{2a}{18}-\frac{3}{b}=\frac{1}{18}\)
\(\frac{3}{b}=\frac{2a}{18}-\frac{1}{18}\)
\(\frac{3}{b}=\frac{2a-1}{18}\)
\(\Leftrightarrow\left(2a-1\right)b=3\times18\)
\(\left(2a-1\right)b=54\)
\(\Rightarrow2a-1;b\in\text{Ư}\left(54\right)\)
Mà 2a là số chẵn
2a - 1 là số lẻ
\(\Rightarrow2a-1\in\text{Ư}l\text{ẻ}\left(54\right)=\left\{\pm1;\pm3;\pm9;\pm27\right\}\)
Ta có bảng :
Vậy các cặp a,b tìm được là :
\(a=1;b=54\)
\(a=0;b=\left(-54\right)\)
\(a=2;b=18\)
\(a=\left(-1\right);b=\left(-18\right)\)
\(a=5;b=6\)
\(a=\left(-4\right);b=\left(-6\right)\)
\(a=14;b=2\)
\(a=\left(-13\right);b=\left(-2\right)\)