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

\(\Leftrightarrow\left(2x^2+x-1\right)\left(2x^2+x-3\right)=0\)

\(\Leftrightarrow\left(2x^2+2x-x-1\right)\left(2x^2+3x-2x-3\right)=0\)

=>(x+1)(2x-1)(2x+3)(x-1)=0

\(\Leftrightarrow x\in\left\{-1;\dfrac{1}{2};-\dfrac{3}{2};1\right\}\)

a) \(A=\left(2x-1\right)\left(x+3\right)-\left(x-2\right)\left(3x-4\right)+5x\)

\(=\left(2x^2+6x-x-3\right)-\left(3x^2-4x-6x+8\right)+5x\)

\(=\left(2x^2+5x-3\right)-\left(3x^2-10x+8\right)+5x\)

\(=2x^2+5x-3-3x^2+10x-8+5x\)

\(=x^2+20x-11\)

b) \(5x\left(2x^2-3x+1\right)-2x\left(x+1\right)\left(x-2\right)\)

\(=10x^3-15x^2+5x-2x\left(x^2-2x+x-2\right)\)

\(=10x^3-15x^2+5x-2x^3+4x^2-2x^2+4x\)

\(=8x^3-13x^2+9x\)

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

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

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

\(C=\left(3x+2\right)\left(x-1\right)-2x\left(x+3\right)-2x+1\\ C=3x^2-x-2-2x^2-6x-2x+1\\ C=x^2-9x-1\)

\(\left(x-2\right)\left(x^2+2x+4\right)-x\left(x-3\right)\left(x+3\right)=10\\ \Leftrightarrow x^3-8-x\left(x^2-9\right)=10\\ \Leftrightarrow x^3-8-x^3-9x=10\\ \Leftrightarrow-9x=18\\ \Leftrightarrow x=-2\)

x=2

(x−2)(x2+2x+4)−x(x−3)(x+3)=10⇔x3−8−x(x2−9)=10⇔x3−8−x3−9x=10⇔−9x=18⇔x=−2

\(A=\dfrac{2}{3}xy^2.\dfrac{3}{2}x\)

\(=x^2y^2\)

Bậc 4

Tại x=-1; y=2

\(\Rightarrow A=x^2y^2=\left(-1\right)^2.2^2=4\)

Ta có: x,y≠0

\(\Rightarrow\left\{{}\begin{matrix}x^2>0\forall x\ne0\\y^2>0\forall y\ne0\end{matrix}\right.\)

\(\Rightarrow x^2y^2>0\forall x,y\ne0\)

a: A=2/3*3/2*xy^2*x=x^2y^2

b: Bậc là 4

c: Khi x=-1 và y=2 thì A=(-1)^2*2^2=4

d: A=(xy)^2>0 khi x<>0 và y<>0

a) ${}^{}-25=0$

${}^{}=0+25=25$

${}^{}={}^{}={}^{}$

$\Rightarrow [\begin{array}{c}2x-1=5\\ 2x-1=-5\end{array}\Rightarrow [\begin{array}{c}2x=6\\ 2x=-4\end{array}\Rightarrow [\begin{array}{c}x=3\\ x=-2\end{array}$

b) $8{}^{}-50x=0$

$2x(4{}^{}$

câu b thiếu bn ơi

ok

a) ${}^{}-25=0$

${}^{}=0+25=25$

${}^{}={}^{}={}^{}$

$\Rightarrow [\begin{array}{c}2x-1=5\\ 2x-1=-5\end{array}\Rightarrow [\begin{array}{c}2x=6\\ 2x=-4\end{array}\Rightarrow [\begin{array}{c}x=3\\ x=-2\end{array}$

b) $8{}^{}-50x=0$

$2x(4{}^{}$

a: Ta có: \(\left(2x-1\right)^2-25=0\)

\(\Leftrightarrow\left(2x-6\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

`2)x^4+2x^3-x^2-2x+1=0`

`<=>x^4+2x^3+x^2-2x^2-2x+1=0`

`<=>(x^2+x)^2-2(x^2+x)+1=0`

`<=>(x^2+x-1)^2=0`

`<=>x^2+x-1=0`

`\Delta=1+4=5`

`=>x_{1,2}=(-1+-sqrt5)/2`

Vậy `S={(-1+sqrt5)/2,(-1+sqrt5)/2`

`3)x^4-4x^3-9x^2+8x+4=0`

`<=>x^4-x^3-3x^3+3x^2-12x^2+12x-4x+4=0`

`<=>(x-1)(x^3-3x^2-12x-4)=0`

`<=>(x-1)(x^3+2x^2-5x^2-10x-2x-4)=0`

`<=>(x-1)(x+2)(x^2-5x-10)=0`

`+)x=1`

`+)x=-2`

`+)x^2-5x-10=0`

`Delta=25+40=65`

`=>x_{12}=(5+sqrt{65})/2`

\(ĐKXĐ:x\ne0;x\ne2\)

\(\frac{4x^2-4x^3+x^4}{x^3-2x^2}=-2\)

\(\Leftrightarrow4x^2-4x^3+x^4=-2\left(x^3-2x^2\right)\)

\(\Leftrightarrow4x^2-4x^3+x^4=-2x^3+4x^2\)

\(\Leftrightarrow x^4-2x^3=0\Leftrightarrow x^3\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\left(ktm\right)\)

Vậy không có x để phân thức bằng -2

Ta có : \(\frac{4x^2-4x^3+x^4}{x^3-2x^2}=-2\)

( ĐKXĐ : \(x\ne0,x\ne\pm\sqrt{2}\) )

\(\Leftrightarrow\frac{4x^2-4x^3+x^4}{x^3-2x^2}+2=0\)

\(\Leftrightarrow4x^2-4x^3+x^4+2\left(x^3-2x^2\right)=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\) ( Loại \(x=0\) không thỏa mãn ĐKXĐ )

Vậy : \(x=2\) thỏa mãn đề.

Yey anh sai :))