A=(2x+3)(x^2-x+2) - 2x(x^2+1/2x-3)

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

=2x^3 - 2x^2 + 4x + 3x^2 - 3x + 6 - 2x^3 - x^2 - 6x

=6 - 5x

ta có : (x+2)^2 + (x-3)^2 - 2(x-3)(x+2)=4x+13

<=> [(x+2) -(x-3)]^2=4x+13

<=>(x+2-x+3)=4x+13

<=>4x+13=5

=>4x= 5-13=-8

=>x=-8/4=-2

Bài 1.

a) -2x( -3x + 2 ) - ( x + 2 )²

= 6x² - 4x - ( x² + 4x + 4 )

= 6x² - 4x - x² - 4x - 4

= 5x² - 8x - 4

b) ( x + 2 )( x² - 2x + 4 ) - 2( x + 1 )( 1 - x )

= x³ + 8 + 2( x + 1 )( x - 1 )

= x³ + 8 + 2( x² - 1 )

= x³ + 8 + 2x² - 2

= x³ + 2x² + 6

c) ( 2x - 1 )² - 2( 4x² - 1 ) + ( 2x + 1 )²

= 4x² - 4x + 1 - 8x² + 2 + 4x² + 4x + 1

= 4

d) x² - 3x + xy - 3y

= x( x - 3 ) + y( x - 3 )

= ( x - 3 )( x + y )

Bài 2.

a) 4x² - 4xy + y² = ( 2x - y )²

b) 9x³ - 9x²y - 4x + 4y

= 9x²( x - y ) - 4( x - y )

= ( x - y )( 9x² - 4 )

= ( x - y )( 3x - 2 )( 3x + 2 )

c) x³ + 2 + 3( x³ - 2 )

= x³ + 2 + 3x³ - 6

= 4x³ - 4

= 4( x³ - 1 )

= 4( x - 1 )( x² + x + 1 )

Bài 3.

2( x - 2 ) = x² - 4x + 4

⇔ ( x - 2 )² - 2( x - 2 ) = 0

⇔ ( x - 2 )( x - 2 - 2 ) = 0

⇔ ( x - 2 )( x - 4 ) = 0

⇔ x = 2 hoặc x = 4

dài quá bạn ơi viết từng câu thôi

mk ko biết làm 

xin lỗi bn nhae

xin lỗi vì đã ko giúp được bn

chcus bn học gioi!

nhae@@@

mình không biết làm

tk nhé@@@@@@@@@@@@@@@@@@@@

LOL

hihi

a) ... \(=\frac{3\left(2x-1\right)+2x\left(3x+3\right)+2x^2+1}{2x\left(2x-1\right)}=\frac{6x-3+6x^2+6x+2x^2+1}{2x\left(2x-1\right)}\)

\(=\frac{8x^2+12x-2}{2x\left(2x-1\right)}=\frac{4x^2+6x-1}{x\left(2x-1\right)}\)(hình như hết đơn giản được rồi, kết quả tạm vậy bạn nhé!)

b) ... \(=\frac{x^3+2x+2x\left(x+1\right)+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\frac{x^3+2x+2x^2+2x+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)

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

c) ... \(=\frac{4\left(x-2\right)+2\left(x+2\right)-5x+6}{\left(x-2\right)\left(x+2\right)}=\frac{4x-8+2x+4-5x+6}{\left(x-2\right)\left(x+2\right)}=\frac{x+2}{\left(x-2\right)\left(x+2\right)}=\frac{1}{x-2}\)

P(x)-Q(x)= 4x³-9x²+5x

7: Ta có: \(\left(3x+4\right)\left(2x-1\right)+6x\left(1-x\right)=0\)

\(\Leftrightarrow6x^2-3x+8x-4+6x-6x^2=0\)

\(\Leftrightarrow11x=4\)

hay \(x=\dfrac{4}{11}\)

8: Ta có: \(2x\left(x^2-1\right)+x\left(-2x^2-3x+1\right)=-x-27\)

\(\Leftrightarrow2x^3-2x-2x^3-3x^2+x+x+27=0\)

\(\Leftrightarrow x^2=9\)

hay \(x\in\left\{3;-3\right\}\)

Bạn sửa lại đề dùm mình nha, sai đề hơi nhiều đó.

ĐKXĐ:\(x\ne0;2\)

\(P=\left(\frac{x^2-2x}{2x^2+8}-\frac{2x^2}{8-4x+2x^2+2x^3}\right)\left(1-\frac{1}{x}-\frac{2}{x^2}\right)\\ P=\left(\frac{x\left(x-2\right)}{2\left(x^2+4\right)}-\frac{2x^2}{4\left(2-x\right)+x^2\left(2-x\right)}\right).\frac{x^2-x-2}{x^2}\\ P=\left(\frac{x\left(x-2\right)}{2\left(x^2+4\right)}+\frac{2x^2}{\left(x^2+4\right)\left(x-2\right)}\right).\frac{x^2-2x+x-2}{x^2}\\ P=\left(\frac{x\left(x-2\right)^2}{2\left(x^2+4\right)\left(x-2\right)}+\frac{4x^2}{2\left(x^2+4\right)\left(x-2\right)}\right).\frac{x\left(x-2\right)+\left(x-2\right)}{x^2}\)

\(P=\frac{x\left(x^2-4x+4\right)+4x^2}{2\left(x^2+4\right)\left(x-2\right)}.\frac{\left(x-2\right)\left(x+1\right)}{x^2}\\ P=\frac{x^3-4x^2+4x-4x^2}{2\left(x^2+4\right)\left(x-2\right)}.\frac{\left(x-2\right)\left(x+1\right)}{x^2}\\ P=\frac{\left(x^3+4x\right)\left(x-2\right)\left(x+1\right)}{2\left(x^2+4\right)\left(x-2\right).x^2}\\ P=\frac{x\left(x^2+4\right)\left(x-2\right)\left(x+1\right)}{2x^2\left(x^2+4\right)\left(x-2\right)}\\ P=\frac{x+1}{2x}\)

 A=5-3(2x+1)^2

Ta có : (2x+1)^2\(\ge\)0

\(\Rightarrow\)-3(2x-1)^2\(\le\)0

\(\Rightarrow\)5+(-3(2x-1)^2)\(\le\)5

Dấu = xảy ra khi : (2x-1)^2=0

=> 2x-1=0 =>x=\(\frac{1}{2}\)

Vậy : A=5 tại x=\(\frac{1}{2}\)

Ta có : (x-1)^2 \(\ge\)0

=> 2(x-1)^2\(\ge\)0

=>2(x-1)^2+3 \(\ge\)3

=>\(\frac{1}{2\left(x-1\right)^2+3}\)\(\le\)\(\frac{1}{3}\)

Dấu = xảy ra khi : (x-1)^2 =0

=> x = 1

Vậy : B = \(\frac{1}{3}\)khi x = 1

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

Làm như câu B                   GTNN = 4 khi x =0 

k vs nha