\(\left(x+1\right)\left(y-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\y-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\y=2\end{cases}}}\)

Vậy .........

\(\left(x-5\right)\left(y-7\right)=1\)

\(\Rightarrow\left(x-5\right);\left(y-7\right)\inƯ\left(1\right)=\left\{-1;1\right\}\)

Xét các trường hợp

Vậy \(\orbr{\begin{cases}\left(x;y\right)=\left(6;8\right)\\\left(x;y\right)=\left(4;6\right)\end{cases}}\)

\(\left(x+4\right)\left(y-2\right)=2\)

\(\Rightarrow\left(x+4\right);\left(y-2\right)\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

Xét các trường hợp :

Vậy...........

1) Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{x+y}{5+7}=\dfrac{48}{12}=4\)

\(\dfrac{x}{5}=4\Rightarrow x=20\\ \dfrac{y}{7}=4\Rightarrow y=28\)

2) Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{4}=\dfrac{y}{-7}=\dfrac{x-y}{4+7}=\dfrac{33}{11}=3\)

\(\dfrac{x}{4}=3\Rightarrow x=12\\ \dfrac{y}{-7}=3\Rightarrow y=-21\)

a) \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7};x+y+z=56\)

\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{56}{14}=4\)

\(\Rightarrow\left\{{}\begin{matrix}x=4.2=8\\y=4.5=20\\z=4.7=28\end{matrix}\right.\)

b) \(\dfrac{x}{1,1}=\dfrac{y}{1,3}=\dfrac{z}{1,4}\left(1\right);2x-y=5,5\)

\(\left(1\right)\Rightarrow\dfrac{2x-y}{1,1.2-1,3}=\dfrac{5,5}{0,9}\)

\(\Rightarrow\left\{{}\begin{matrix}x=1,1.\dfrac{5,5}{0,9}=\dfrac{6,05}{0,9}\\y=1,3.\dfrac{5,5}{0,9}=\dfrac{7,15}{0,9}\\z=\dfrac{1,4}{1,1}.x=\dfrac{1,4}{1,1}.\dfrac{6,05}{0,9}=\dfrac{8,47}{0,99}\end{matrix}\right.\)

d) \(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5};xyz=-30\)

\(\dfrac{x}{2}=\dfrac{x}{3}=\dfrac{z}{5}=\dfrac{xyz}{2.3.5}=\dfrac{-30}{30}=-1\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-1\right)=-2\\y=3.\left(-1\right)=-3\\z=5.\left(-1\right)=-5\end{matrix}\right.\)

a) �2=�5=�7;�+�+�=562x​=5y​=7z​;x+y+z=56

�2=�5=�7=�+�+�2+5+7=5614=42x​=5y​=7z​=2+5+7x+y+z​=1456​=4

⇒{�=4.2=8�=4.5=20�=4.7=28⇒⎩⎨⎧​x=4.2=8y=4.5=20z=4.7=28​

b) �1,1=�1,3=�1,4(1);2�−�=5,51,1x​=1,3y​=1,4z​(1);2x−y=5,5

(1)⇒2�−�1,1.2−1,3=5,50,9(1)⇒1,1.2−1,32x−y​=0,95,5​
    

⇒⎩⎨⎧​x=1,1.0,95,5​=0,96,05​y=1,3.0,95,5​=

chết rùi nó bị lỗi

xin lỗi nha

Ta có : \(\frac{x}{4}=\frac{y}{7}\) 

\(\Rightarrow\frac{x^2}{16}=\frac{y^2}{49}=\frac{3x^2}{48}=\frac{4y^2}{196}=\frac{3x^2-4y^2}{48-196}=\frac{100}{-148}=-\frac{25}{37}\)

Thay vào là ra nhé !:D

Cái chỗ Nguyễn Quang Trung đúng ròi

\(\Rightarrow\hept{\begin{cases}\frac{x}{4}=-\frac{25}{37}\\\frac{y}{7}=-\frac{25}{37}\end{cases}}\Rightarrow\hept{\begin{cases}x=-\frac{100}{37}\\y=-\frac{175}{37}\end{cases}}\)

d: x+y=5

nên x=5-y

Ta có: xy=6

=>y(5-y)=6

=>y²-5y+6=0

=>(y-2)(y-3)=0

=>y=2 hoặc y=3

=>x=3 hoặc x=2

a: \(\Leftrightarrow\left(x-3;y+4\right)\in\left\{\left(1;-7\right);\left(-1;7\right);\left(-7;1\right);\left(7;-1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(4;-11\right);\left(2;3\right);\left(-4;-3\right);\left(10;-5\right)\right\}\)

chịu