a: \(\left(x+\dfrac{1}{4}\right)+\left(3x-4\right)+2\left(x-3\right)=1\)

=>\(x+\dfrac{1}{4}+3x-4+2x-6=1\)

=>\(6x-\dfrac{39}{4}=1\)

=>\(6x=1+\dfrac{39}{4}=\dfrac{43}{4}\)

=>\(x=\dfrac{43}{4}:6=\dfrac{43}{24}\)

b: \(2\left(x-3\right)=3\left(x+2\right)-x+1\)

=>\(2x-6=3x+6-x+1\)

=>2x-6=2x+7

=>-6=7(vô lý)

c: \(x\left(x+3\right)+x\left(x-2\right)=2x\left(x-1\right)\)

=>\(x^2+3x+x^2-2x=2x^2-2x\)

=>3x-2x=-2x

=>3x=0

=>x=0

d: \(\left(x-1\right)\cdot3x-2\left(x+2\right)-2x=x\left(x-1\right)\)

=>\(3x^2-3x-2x-4-2x=x^2-x\)

=>\(3x^2-7x-4-x^2+x=0\)

=>\(2x^2-6x-4=0\)

=>\(x^2-3x-2=0\)

=>\(x=\dfrac{3\pm\sqrt{17}}{2}\)

Tui làm bài hình thôi nha.

a/ Ta có: \(\hept{\begin{cases}\widehat{xOm}=\widehat{nOy}=90^0\left(gt\right)\\\widehat{nOm}:chung\end{cases}\Rightarrow\widehat{xOn}=\widehat{mOy}}\)

b/ Vì Ot là pgiác góc xOy => góc xOt = góc tOy

Mà: góc xOn = góc mOy (cmt)

=> góc nOt = góc tOm

=> Ot là phân giác góc nOm

A ) x = 5/24

B ) x = 7/15

Bài 2:

Ta có: \(\left.\begin{matrix} \frac{x}{4} = \frac{y}{5} & & \\ \frac{y}{5} = \frac{z}{2} & & \end{matrix}\right\}\)

=> \(\frac{x}{4} = \frac{y}{5} = \frac{z}{2}\)

Theo tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{x}{4} = \frac{y}{5} = \frac{z}{2} = \frac{x - y + z}{4 - 5 + 2}= \frac{98}{1}= 98\)

=> x = 98 * 4 = 392

y = 98 * 5 = 490

z = 196

Vậy x = 392, y = 490, z = 196

Bài 3:

Gọi x,y lần lượt là số cây trồng của lớp 7A, 7B

Theo đề bài ta có: \(\frac{x}{4} = \frac{y}{5}\) và y - x = 12

Theo tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{x}{4} = \frac{y}{5}= \frac{y - x}{5 - 4}= \frac{12}{1}= 12\)

=> x = 12 * 4 = 48

y = 12 * 5= 60

Vậy lớp 7A trồng 48 cây

.......lớp 7B trồng 60 cây

Bài 1 câu g bạn kia làm sai mình sửa lại nhá

\(3a^2-6ab+3b^2-12c^2\)

\(=3\left(a^2-2ab+b^2\right)-12c^2\)

\(=3\left(a-b\right)^2-12c^2\)

\(=3\left[\left(a-b\right)^2-4c^2\right]\)

\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)

Để mình làm tiếp cho :))

Bài 2 :

Câu a : \(37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5\)

\(=\left(37,5.8,5+1,5.37,5\right)-\left(7,5.3,4+6,6.7,5\right)\)

\(=37,5\left(8,5+1,5\right)-7,5\left(3,4+6,6\right)\)

\(=37,5.10-7,5.10\)

\(=10.30=300\)

Câu b : \(35^2+40^2-25^2+80.35\)

\(=\left(35^2+80.35+40^2\right)-25^2\)

\(=\left(30+45\right)^2-25^2\)

\(=75^2-25^2\)

\(=\left(75+25\right)\left(75-25\right)\)

\(=100.50=5000\)

Bài 3 :

Câu a : \(x^3-\dfrac{1}{9}x=0\)

\(\Leftrightarrow x\left(x^2-\dfrac{1}{9}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{1}{9}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{1}{3}\end{matrix}\right.\)

Câu b : \(2x-2y-x^2+2xy-y^2=0\)

\(\Leftrightarrow2\left(x-y\right)-\left(x-y\right)^2=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-y=0\\2-x+y=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=y\\x+y=2\Rightarrow x=2-y\end{matrix}\right.\)

Câu c :

\(x\left(x-3\right)+x-3=0\)

\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

\(x^2\left(x-3\right)+27-9x=0\)

\(\Leftrightarrow x^2\left(x-3\right)-9\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(x^2-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=\pm3\end{matrix}\right.\)

Bài 4 :

Câu a :

\(x^2-4x+3\)

\(=x^2-x-3x+3\)

\(=\left(x^2-x\right)-\left(3x-3\right)\)

\(=x\left(x-1\right)-3\left(x-1\right)\)

\(=\left(x-1\right)\left(x-3\right)\)

Câu b :

\(x^2+x-6\)

\(=x^2-2x+3x-6\)

\(=x\left(x-2\right)+3\left(x-2\right)\)

\(=\left(x-2\right)\left(x+3\right)\)

Câu c :

\(x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=\left(x^2-2x\right)-\left(3x-6\right)\)

\(=x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\left(x-3\right)\)

Câu d :

\(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

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

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

Bài 1:

a) \(2x^2-2xy-5x+5y\)

\(=\left(2x^2-2xy\right)-\left(5x-5y\right)\)

\(=2x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(2x-5\right)\)

b) \(8x^2+4xy-2ax-ay\)

\(=\left(8x^2+4xy\right)-\left(2ax+ay\right)\)

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

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

c) \(x^3-4x^2+4x\)

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

\(=x\left(x-2\right)^2\)

d) \(2xy-x^2-y^2+16\)

\(=-\left[\left(x^2-2xy+y^2\right)-16\right]\)

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

\(=-\left[\left(x-y-4\right)\left(x-y+4\right)\right]\)

e) \(x^2-y^2-2yz-z^2\)

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

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

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

g) \(3a^2-6ab+3b^2-12c^2\)

\(=\left(3a^2-6ab+3b^2\right)-12c^2\)

\(=\left(\sqrt{3a}+\sqrt{3b}\right)^2-12c^2\)

\(=\left(\sqrt{3a}+\sqrt{3b}+\sqrt{12c}\right)\left(\sqrt{3a}+\sqrt{3b}-\sqrt{12c}\right)\)

 (x + 1) + (x + 2) + (x + 3 )+ ... + (x + 20) = 250 ( có 20 nhóm )
=> ( x + x + x +...+ x ) + ( 1 + 2 + 3 +...+ 20) = 250 ( có 20 x và 20 số hạng )
=> x . 20 + 20 . 21 : 2 = 250
=> x . 20 + 210 = 250
=> x . 20 = 250 - 210
=> x . 20 = 40
=> x = 40 : 20
     x = 2

(x+1)+(x+2)+(x+3)+...+(x+20)=250

Dãy trên có 20 số hạng

20x+(1+2+3+...+20)=250

Tổng dãy 1+2+3+...+20 là

(20+1).20:2=210

20x+210=250

20x=250-210

20x=40

x=40:20

x=2

(x + 1) + (x + 2) + (x + 3 )+ ... + (x + 20) = 250

250 = ( 1 + 2 + 3 + ... + 20 ) + ( 20 x x )

250 = 210 + ( 20 x X ) 

X = ( 250 - 210 ) : 20

X = 2. k mình nha

Lời giải  đầy đủ:

Bài 3:tìm x

A,

6.(x+9845)=29042.6

(x+9845)=29042.6:6

x+9845=29042

x=29042-9845

x=19197.

B,

(x:3).8=8.3198

(x:3)=3198.8:8

x:3=3198

x=3198.3

x=9594.

Bài 7:

A/191+x+9=43.5

200+x=215

x=215-200

x=15.

B/x.25.4=125.8

x.100=1000

x=1000:100

x=10.

Bài 8:

A/ 128.x-12.x-16.x=5208000

(128-12-16).x=5208000

100.x=5208000

x=5208000:100

x=52080.

B/ x.27+x.30+x.43=210500

x.(27+30+43)=210500

x.100=210500

x=210500:100

x=2105.

K mình nhé!