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16 tháng 4 2022

Mình có 2 cách lận nhưng theo mình nghĩ cách này dễ nhất.

-OD cắt AB tại G; OF cắt AC tại H, OE cắt BC tại I.

-GO//BF, BG//OF \(\Rightarrow\)BGOF là hình bình hành \(\Rightarrow OF=BG\Rightarrow\dfrac{OF}{AB}=\dfrac{BG}{AB}\left(1\right)\).

-\(\dfrac{OE}{AC}=\dfrac{OE}{EI}.\dfrac{EI}{AC}=\dfrac{GE}{BE}.\dfrac{BE}{AB}=\dfrac{GE}{AB}\left(2\right)\).

-OI//DC, OD//IC \(\Rightarrow\)ODCI là hình bình hành.\(\Rightarrow OD=IC\Rightarrow\dfrac{OD}{BC}=\dfrac{IC}{BC}=\dfrac{AE}{AB}\left(3\right)\)

-Từ (1) ,(2), (3) suy ra:\(\dfrac{OD}{BC}+\dfrac{OE}{CA}+\dfrac{OF}{AB}=\dfrac{BG}{AB}+\dfrac{GE}{AB}+\dfrac{AE}{AB}=\dfrac{AB}{AB}=1\)

Gọi giá loại vở 2 là x

=>Giá loại vở 1 là x+300

Theo đề, ta có: \(\dfrac{12000}{x}-\dfrac{12000}{x+300}=2\)

=>\(12000x+3600000-12000x=2x\left(x+300\right)\)

=>2x^2+600x=3600000

=>x=1200

=>Giá loại 1 là 1500 đồng

17 tháng 2 2023

mình cảm ơn nhiều ạ

 

HQ
Hà Quang Minh
Giáo viên
1 tháng 8 2023

Bài 1:

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

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

\(c,3a^2-6ab+3b^2-12c^2=3\left(a-b\right)^2-12c^2=3\left[\left(a-b\right)^2-4c^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)

\(d,x^2-25+y^2+2xy=\left(x-y\right)^2-25=\left(x-y-5\right)\left(x-y+5\right)\)

HQ
Hà Quang Minh
Giáo viên
1 tháng 8 2023

Bài 1:

\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b-c\right)\left(a+b\right)\)

\(f,x^2-2x-4y^2-4y=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x-2y-2\right)\left(x+2y\right)\)

\(g,x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)

\(h,x^2\left(x-1\right)+16\left(1-x\right)=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)

18 tháng 7 2023

1) \(\left(x+\dfrac{1}{3}\right)^3=x^3+3.x^2.\dfrac{1}{3}+3.x.\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)^3\)

\(=x^3+x^2+\dfrac{x}{3}+\dfrac{1}{27}\)

2) \(\left(2x+y^2\right)^3=\left(2x\right)^3+3.\left(2x\right)^2.y^2+3.2x.\left(y^2\right)^2+\left(y^2\right)^3\)

\(=8x^3+12x^2y^2+6xy^4+y^6\)

3) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}y\right)^3=\left(\dfrac{1}{2}x^2\right)^3+3.\left(\dfrac{1}{2}x^2\right)^2.\dfrac{1}{3}y+3.\dfrac{1}{2}x^2.\left(\dfrac{1}{3}y\right)^2+\left(\dfrac{1}{3}y\right)^3\)

\(=\dfrac{1}{8}x^6+\dfrac{1}{4}x^4y+\dfrac{1}{6}x^2y^2+\dfrac{1}{27}y^3\)

4) \(\left(3x^2-2y\right)^3=\left(3x^2\right)^3-3.\left(3x^2\right)^2.2y+3.3x^2.\left(2y\right)^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3\)

5) \(\left(\dfrac{2}{3}x^2-\dfrac{1}{2}y\right)^3=\left(\dfrac{2}{3}x^2\right)^3-3.\left(\dfrac{2}{3}x^2\right)^2.\dfrac{1}{2}y+3.\dfrac{2}{3}x^2.\left(\dfrac{1}{2}y\right)^2-\left(\dfrac{1}{2}y\right)^3\)

\(=\dfrac{8}{27}x^6-\dfrac{1}{3}x^4y+\dfrac{1}{2}x^2y^2-\dfrac{1}{8}y^3\)

6) \(\left(2x+\dfrac{1}{2}\right)^3=\left(2x\right)^3+3.\left(2x\right)^2.\dfrac{1}{2}+3.2x.\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3\)

\(=8x^3+6x^2+\dfrac{3}{2}x+\dfrac{1}{8}\)

7) \(\left(x-3\right)^3=x^3-3.x^2.3+3.x.3^2-3^3\)

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

18 tháng 7 2023

8) \(\left(x+1\right)\left(x^2-x+1\right)\)

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

\(=x^3+1^3\)

\(=x+1\)

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

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

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

\(=x^3-27\)

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

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

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

\(=x^3-8\)

11) \(\left(x+4\right)\left(x^2-4x+16\right)\)

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

\(=x^3+4^3\)

\(=x^3+64\)

12) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

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

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

\(=x^3-27y^3\)

13) \(\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\)

\(=\left(x^2-\dfrac{1}{3}\right)\left[\left(x^2\right)^2+x^2.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2\right]\)

\(=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3\)

\(=x^6-\dfrac{1}{27}\)

14) \(\left(\dfrac{1}{3}x+2y\right)\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)\)

\(=\left(\dfrac{1}{3}x+2y\right)\left[\left(\dfrac{1}{3}x\right)^2-\dfrac{1}{3}x.2y+\left(2y\right)^2\right]\)

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

\(=\dfrac{1}{27}x^3+8y^3\)

a: \(\Leftrightarrow2x\left(x+2\right)+4>x^2+4x+4\)

\(\Leftrightarrow2x^2+4x-x^2-4x>0\)

=>x<>0

b: \(\Leftrightarrow3\left(1-2x\right)-24x< 4\left(1-5x\right)\)

=>3-6x-24x<4-20x

=>-30x+3<4-20x

=>-10x<1

hay x>-1/10

c: \(\Leftrightarrow x^2+6x+8>x^2+10x+16+26\)

=>6x+8>10x+42

=>-4x>34

hay x<-17/2

3:

a: \(M=x+2x-4y-y-3=3x-5y-3\)

bậc là 1

b: \(N=-x^2t+13t^3+xt^2+5t^3-4\)

bậc là 3

5:

S=(3x+4y)*2*2z=4z(3x+4y)

V=3x*4y*2z=24xyz

Khi x=4;y=2;z=1 thì S=4*1*(3*4+4*2)=4*20=80cm2

V=24*4*2*1=192cm3

\(A=\left(\dfrac{4}{\left(x-2\right)\left(x+2\right)}+2\right)\cdot\dfrac{x+2}{2x}+\dfrac{2}{x-2}\)

\(=\dfrac{4+2x^2-8}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{2x}+\dfrac{2}{x-2}\)

\(=\dfrac{2\left(x^2-2\right)}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x+2}{2x}+\dfrac{2}{x-2}\)

\(=\dfrac{\left(x^2-2\right)}{x\left(x-2\right)}+\dfrac{2}{x-2}\)

\(=\dfrac{x^2+2x-2}{x\left(x-2\right)}\)

26 tháng 7 2023

D nha bạn

 

25 tháng 10 2021

a: \(\dfrac{5x^2+10xy+5y^2}{3x^3+3y^3}\)

\(=\dfrac{5\left(x+y\right)^2}{3\left(x+y\right)\left(x^2-xy+y^2\right)}\)

\(=\dfrac{5\left(x+y\right)}{3\left(x^2-xy+y^2\right)}\)

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

\(=6x^2-3x-6x^2-4x-3x-2\)

\(=-10x-2\)

25 tháng 10 2021

bạn có thể giúp mik bài 2 đc ko