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28 tháng 5 2017

Câu 1:

\(3x\left(12x+4\right)+9x\left(4x+3\right)\)

\(\Leftrightarrow3x\left(12x+4\right)+3x\left[3.\left(4x+3\right)\right]\)

\(\Leftrightarrow3x\left(12x+4\right)+3x\left(12x+6\right)\)

\(\Leftrightarrow3x\left[12x+4+12x+6\right]\)

\(\Leftrightarrow3x.\left(24x+10\right)\)

\(\Leftrightarrow72x^2+30x\)

Câu 2:

\(x\left(5+2x\right)+2x^2\left(x-1\right)\)

\(\Leftrightarrow5x+2x^2+2x^3-2x^2\)

\(\Leftrightarrow2x^3+5x\)

28 tháng 5 2017

Đề 1

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Examples by Topic Quick video overview

Input:

 
1>3 x (12 x + 4) + 9 x (4 x + 3)

Open code

 
 
 

Inequality plot:

 
 
| | 1  | 3 x (24 x + 13)

Open code

 
EnlargeDataCustomizeA PlaintextInteractive
 

Alternate forms:

1>3 x (24 x + 13)

Open code

 
 
3 x (24 x + 13)<1

Open code

 
 
768/67 (x + 13/48)^2<1
 
 
 

Expanded form:

1>72 x^2 + 39 x

Open code

 
 
 

Solution:

  • Approximate form
1/48 (-13 - sqrt(201))<x<1/48 (sqrt(201) - 13)

Open code

 
 
 

Integer solution:

x = 0

Open code

 
 
 
17 tháng 8 2020

a, \(12-2\left(1-x\right)^2=\left(3x-2\right)\left(2x-3\right)\)

\(< =>12-2\left(1-2x+x^2\right)=6x^2-9x-4x+6\)

\(< =>12-2+4x-2x^2=6x^2-13x+6\)

\(< =>10+4x-2x^2-6x^2+13x-6=0\)

\(< =>-8x^2+17x+4=0< =>\orbr{\begin{cases}x=\frac{17-\sqrt{417}}{16}\\x=\frac{17+\sqrt{417}}{16}\end{cases}}\)

b, \(10x+3-5x=4x+12< =>5x+3-4x-12=0\)

\(< =>x-9=0< =>x=9\)

c, \(11x+42-2x=100-9x-22< =>9x+42-100+9x+22=0\)

\(< =>18x+64-100=0< =>18x-36=0< =>x=\frac{36}{18}=2\)

d, \(2x-\left(3-5x\right)=4\left(x+3\right)< =>2x-3+5x=4x+12\)

\(< =>7x-3-4x-12=0< =>3x-15=0< =>x=\frac{15}{3}=5\)

e, \(2\left(x-3\right)+5x\left(x-1\right)=5x^2< =>2x-6+5x^2-5=5x^2\)

\(< =>2x-11+5x^2-5x^2=0< =>2x-11=0< =>x=\frac{11}{2}\)

f, \(-6\left(1,5-2x\right)=3\left(-15+2x\right)< =>-6\left(\frac{3}{2}-2x\right)=3\left(2x-15\right)\)

\(< =>-9+12x-6x+45=0< =>6x+36=0< =>x=-6\)

g, \(14x-\left(2x+7\right)=3x+12x-13< =>14x-2x-7=15x-13\)

\(< =>12x-7-15x+13=0< =>-3x+6=0< =>x=-2\)

h, \(\left(x-4\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)

\(< =>x^2-16-6x+4=x^2-8x+16\)

\(< =>x^2-6x-12-x^2+8x-16=0\)

\(< =>2x-28=0< =>x=\frac{28}{2}=14\)

q, \(4\left(x-2\right)-\left(x-3\right)\left(2x-5\right)=?\)thiếu đề

19 tháng 10 2020

a) Đặt t = x2

bthuc <=> t2 - 7t + 16 

Từ đây ta không thể phân tích được :)

b) x3 - 2x2 + 5x - 4 

= x3 - x2 - x2 + x + 4x - 4

= x2( x - 1 ) - x( x - 1 ) + 4( x - 1 )

= ( x - 1 )( x2 - x + 4 )

c) x3 - 2x2 + x - 3 ( phân tích hổng ra :)) )

d) 3x3 - 4x2 + 12x - 4 ( phân tích hổng ra p2 :)) )

e) 6x3 + x2 + x + 1

= 6x3 + 3x2 - 2x2 - x + 2x + 1

= 3x2( 2x + 1 ) - x( 2x - 1 ) + ( 2x + 1 )

= ( 2x + 1 )( 3x2 - x + 1 )

f) 4x3 + 6x2 + 4x + 1

= 4x3 + 2x2 + 4x2 + 2x + 2x + 1

= 2x2( 2x + 1 ) + 2x( 2x + 1 ) + ( 2x + 1 )

= ( 2x + 1 )( 2x2 + 2x + 1 )

19 tháng 10 2020

:) Quỳnh đặt ĐK đi nè :3 \(x^2=t\left(t\ge0\right)\)

12 tháng 7 2019

a,\(xy+3x-7y-21\)

\(=x\left(y+3\right)-7\left(y+3\right)\)

\(=\left(y+3\right)\left(x-7\right)\)

12 tháng 7 2019

\(b,2xy-15-6x+5y\)

\(=\left(2xy-6x\right)+\left(-15+5y\right)\)

\(=2x\left(y-3\right)-5\left(3-y\right)\)

\(=2x\left(y-3\right)+5\left(y-3\right)\)

\(=\left(y-3\right)\left(2x+5\right)\)

11 tháng 5 2020

\(x^3-6x^2+5x+12>0\\ < =>\left(x^3-5x-x+5x\right)+12>0\\ < =>\left[\left(x^3-x\right)-\left(5x-5x\right)\right]+12>0\\ < =>x^2+12>0\\ < =>x^2>-12\\ =>x\in R\\ BPTcóvôsốnghiem\)