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

Mk cần gấp để nộp ạ

a)  \(3a=2b\)\(\Rightarrow\)\(\frac{a}{2}=\frac{b}{3}\) hay  \(\frac{a}{10}=\frac{b}{15}\)

\(4b=5c\)\(\Rightarrow\)\(\frac{b}{5}=\frac{c}{4}\)  hay  \(\frac{b}{15}=\frac{c}{12}\)

suy ra:   \(\frac{a}{10}=\frac{b}{15}=\frac{c}{12}\)

đến đây bạn áp dụng tính chất dãy tỉ số bằng nhau nha

b)  \(\left|x-1\right|+\left|y+\frac{2}{3}\right|+\left|x^2+xz\right|=0\)

Nhận thấy:   \(\left|x-1\right|\ge0\)    \(\left|y+\frac{2}{3}\right|\ge0;\) \(\left|x^2+xz\right|\ge0\)

suy ra:   \(\left|x-1\right|+\left|y+\frac{2}{3}\right|+\left|x^2+xz\right|\ge0\)

Dấu "=" xảy ra  \(\Leftrightarrow\)\(\hept{\begin{cases}x-1=0\\y+\frac{2}{3}=0\\x^2+xz=0\end{cases}}\)\(\Leftrightarrow\)\(\hept{\begin{cases}x=1\\y=-\frac{2}{3}\\z=-1\end{cases}}\)

Vậy....

a) \(\left(xy+1\right)^2-\left(x+y\right)^2\)

\(=\left(xy+1-x+y\right)\left(xy+1+x-y\right)\)

b) \(\left(x+y\right)^3-\left(x-y\right)^3\)

\(=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)

\(=\left(x+y-x+y\right)\left[\left(x^2+2xy+y^2\right)+x^2-y^2+\left(x^2-2xy+y^2\right)\right]\)

\(=2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)

\(=2y\left(3x^2+y^2\right)\)

c) \(3x^4y^2+3x^3y^2+3xy^2+3y^2\)

\(=3y^2\left(x^4+x^3+x+1\right)\)

d) \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)

\(=4\left[\left(x^2-y^2\right)-2\left(x-ay\right)-\left(a^2-1\right)\right]\)

\(=4\left[\left(x^2-y^2\right)-\left(2x-2ay\right)-\left(a^2-1\right)\right]\)

\(=4\left(x^2-y^2-2x+2ay-a^2+1\right)\)

P/s: Ko chắc!

c/

\(=3y^2\left(x^4+x^3+x+1\right)\)

\(=3y^2\left[x^3\left(x+1\right)+x+1\right]\)

\(=3y^2\left(x^3+1\right)\left(x+1\right)\)

\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)

d/

\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)

\(=4\left(x-1\right)^2-4\left(y-a\right)^2\)

\(=4\left[\left(x-1\right)^2-\left(y-a\right)^2\right]\)

\(=4\left(x-1-y+a\right)\left(x-1+y-a\right)\)

Bài 1: 

Ta có:

\(y-x=25\Rightarrow y=25+x\)

Mà \(7x=4y\Rightarrow7x=4\cdot\left(25+x\right)\)

\(7x=100+4x\)

\(\Rightarrow7x-4x=100\)

\(3x=100\)

\(x=\frac{100}{3}\)

bài 1 :

Ta có: 7x=4y ⇔ x/4=y/7

áp dụng tính chất dãy tỉ số bằng nhau ta có 

x/4=y/7=(y-x)/(7-4)=100/3

⇒x= 4 x 100/3=400/3 ; y = 7 x 100/3=700/3

bài 2 

ta có x/5 = y/6 ⇔ x/20=y/24

         y/8 = z/7 ⇔ y/24=z/21

⇒x/20=y/24=z/21

ADTCDTSBN(bài 1 có)

x/20=y/24=z/21=(x+y)/(20+24)=69/48=23/16

⇒x= 20 x 23/16 = 115/4

   y= 24x 23/16=138/2

   z=21x23/16=483/16

bài 3

x:y:z=3:8:5  ⇔ x/3=y/8=z/5

ADTCDTSBN

x/3=y/8=z/5=(3x+y-4z)/(9+8-10)=14/7=2

⇒x = 2x3 = 6 ; y= 2x8=`16; z=2x5=10