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\(\dfrac{x-1}{9}+\dfrac{1}{3}=\dfrac{1}{y+2}\)
\(\dfrac{x-1}{9}+\dfrac{3}{9}=\dfrac{1}{y+2}\)
\(\dfrac{x-1+3}{9}=\dfrac{1}{y+2}\)
\(\dfrac{x-\left(1-3\right)}{9}=\dfrac{1}{y+2}\)
\(\dfrac{x-\left(-2\right)}{9}=\dfrac{1}{y+2}\)
\(\dfrac{x+2}{9}=\dfrac{1}{y+2}\)
\(\left(x+2\right)\left(y+2\right)=9\)
=> (X+2) ; (y+2) ϵ Ư(9)
TH1: x+2 = 1 => x = -1
y+2=9 => y = 7
TH2: x+2 = 9 => x = 7
=> y +2 = 1 => y =-1
TH3:x+2 = -9 => x = -11
y+2 = -1 => y=-3
TH4: x+2 = -1 => x =-3
y+2 = -9 => x=-11
TH5: x+2 = -3 => x =-5
y+2 = -3 => y=-5
TH6: x+2 =3 => x = 1
y+2=3 => y=1
Ta có: \(x+y+z=18\)
\(\dfrac{x+1}{3}=\dfrac{y+2}{5}=\dfrac{z+3}{5}\)
\(\Rightarrow\dfrac{x+1}{3}=\dfrac{y+2}{5}=\dfrac{z+3}{5}and=\dfrac{\left(y+z\right)+\left(2+3\right)}{5}+\dfrac{\left(x+1\right)}{3}\)
\(\Leftrightarrow\dfrac{5+\left(y+z\right)}{5}+\dfrac{1+x}{3}\)
\(and\dfrac{5}{5}=1\)
\(\Rightarrow x=1-\dfrac{1}{3}=\dfrac{2}{3}\) vậy \(x=2\)
Ps: tự làm tiếp nha mình mới làm tới đó
\(y+30\%y=-1,3\\ 130\%y=-1,3\\ \Rightarrow y=\dfrac{-1,3}{130\%}=-1\)
\(x:\dfrac{4}{28}=\dfrac{13}{-19}+\dfrac{8}{25}\\ 7x=-\dfrac{173}{475}\\ x=-\dfrac{\dfrac{173}{475}}{7}=-\dfrac{173}{3325}\)
b)3x+1/18+2y/12=2/9 và x-y=1
2(3x+1)/18x2+2y x 3/12x3=2x4/9x4
6x+2+6y=8
6x+6y=8-2=6
6(x+y)=6
x+y=6:6=1(1)
theo đề bài ta có:x-y=1 suy ra x=y+1
thay x=y+1 vào (1)
y+1+y=1
2y=1-1=0
y=0:2=0
x=0+1=1
xong rồi câu a) ko biết làm
a) <=> \(\dfrac{x-1}{9}+\dfrac{1}{3}=\dfrac{1}{y+2}\Leftrightarrow x-1+2=\dfrac{9}{y+2}\)
\(\Leftrightarrow x=\dfrac{9}{y+2}-1\) với mỗi giá trị của y khác -2 luôn tìm được x
từ và x-y =1 áp cho cả câu (a) thì
\(x-y=1=>x+1=y+2\)
\(y+2=\dfrac{9}{y+2}\Leftrightarrow\left\{{}\begin{matrix}y\ne-2\\\left(y+2\right)^2=9\end{matrix}\right.\)
y+2 = 3 => y = 1 =>x=2
y+2 =-3 => y =-5=> x=-4
2)\(x+y+z=9^2=81\)
Ta có:\(\dfrac{x}{3}=\dfrac{y}{4}\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}\left(1\right)\)
\(\dfrac{y}{5}=\dfrac{z}{7}\Rightarrow\dfrac{y}{20}=\dfrac{z}{28}\left(2\right)\)
Từ (1) và (2)\(\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}\)
\(\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}=\dfrac{x+y+z}{15+20+28}=\dfrac{81}{63}=\dfrac{9}{7}\)
\(\Rightarrow x=\dfrac{135}{7};y=\dfrac{180}{7};z=36\)
a) \(\dfrac{-5}{6}.\dfrac{120}{25}< x< \dfrac{-7}{15}.\dfrac{9}{14}\)
\(\Rightarrow-4< x< \dfrac{-3}{10}\)
\(\Rightarrow\dfrac{-40}{10}< x< \dfrac{-3}{10}\)
\(\Rightarrow x\in\left\{\dfrac{-39}{10};\dfrac{-38}{10};\dfrac{-37}{10};...;\dfrac{-5}{10};\dfrac{-4}{10}\right\}\)
b) \(\left(\dfrac{-5}{3}\right)^2< x< \dfrac{-24}{35}.\dfrac{-5}{6}\)
\(\Rightarrow\dfrac{25}{9}< x< \dfrac{4}{7}\)
\(\Rightarrow\dfrac{175}{63}< x< \dfrac{36}{63}\)
\(\Rightarrow x=\varnothing\)
c) \(\dfrac{1}{18}< \dfrac{x}{12}< \dfrac{y}{9}< \dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{2}{36}< \dfrac{3x}{36}< \dfrac{4y}{36}< \dfrac{9}{36}\)
\(\Rightarrow x\in\left\{1;2\right\}\)
+) Với \(x=1\)
\(\Rightarrow y\in\left\{1;2\right\}\)
+) Với \(x=2\)
\(\Rightarrow y=2\)
Vậy \(x=1\) thì \(y\in\left\{1;2\right\}\); \(x=2\) thì \(y=8\).
\(\dfrac{x}{9}=\dfrac{3}{y}+\dfrac{1}{18}\left(y\ne0\right)\)
\(\Rightarrow\dfrac{2xy}{18y}=\dfrac{54}{18y}+\dfrac{y}{18y}\)
\(\Rightarrow2xy=54+y\)
\(\Rightarrow2xy-y=54\)
\(\Rightarrow xy-\dfrac{y}{2}=27\)
\(\Rightarrow y\left(x-\dfrac{1}{2}\right)=27\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right);y\in\left\{1;3;9;27\right\}\)
\(\Rightarrow\left(x;\right)y\in\left\{\left(\dfrac{1}{2};27\right);\left(\dfrac{5}{2};9\right);\left(\dfrac{17}{2};3\right);\left(\dfrac{53}{2};1\right)\right\}\)
\(\Rightarrow\left(x;y\right)\in\varnothing\left(x;y\inℕ\right)\)