b: Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)

\(\Leftrightarrow\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=0\)

\(\Leftrightarrow\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24=0\)

\(\Leftrightarrow x^2+7x+6=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-6\end{matrix}\right.\)

Ta có : \(x\left(x+1\right)\left(x-1\right)\left(x+2\right)=24\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2-x+2x-2\right)=24\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)=24\)

\(\Leftrightarrow\left(x^2+x-1+1\right)\left(x^2+x-1-1\right)=24\)

\(\Leftrightarrow\left(x^2+x-1\right)^2-1=24\)

\(\Leftrightarrow\left(x^2+x-1\right)^2=25\)

<=> 2 trường hợp sảy ra là bằng 5 hoặc -5 nhé 

bạn lam được cả câu a thì mk k

a,

\(x^4+2x^3+3x^2+2x+1-3x^4-3x^2-3=0.\)

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

\(x^4-x^3-x+1=0\)  " chia cả 2 vế cho -2 )

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

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

\(\hept{\begin{cases}x=1\\x^3=1\end{cases}}\)

Câu a:

\(x(x+1)(x^2+x+1)=42\)

\(\Leftrightarrow (x^2+x)(x^2+x+1)=42\)

Đặt \(x^2+x=a\) thì pt trở thành: \(a(a+1)=42\)

\(\Leftrightarrow a^2+a-42=0\Leftrightarrow (a-6)(a+7)=0\)

\(\Rightarrow \left[\begin{matrix} a=6\\ a=-7\end{matrix}\right.\)

Nếu $a=6$ \(\leftrightarrow x^2+x=6\leftrightarrow x^2+x-6=0\leftrightarrow (x-2)(x+3)=0\)

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

Nếu $a=-7$

\(\leftrightarrow x^2+x=-7\Leftrightarrow x^2+x+7=0\)

\(\Leftrightarrow (x+\frac{1}{2})^2+\frac{27}{4}=0\) (vô lý)

Vậy pt có nghiệm \(x=2\) hoặc $x=-3$

Câu b:

\(x(x+1)(x+2)(x+3)=24\)

\(\Leftrightarrow [x(x+3)][(x+1)(x+2)]=24\)

\(\Leftrightarrow (x^2+3x)(x^2+3x+2)=24\)

Đặt \(x^2+3x=a\) thì pt trở thành: \(a(a+2)=24\)

\(\Leftrightarrow a^2+2a+1=25\Leftrightarrow (a+1)^2=25\)

\(\Rightarrow a+1=\pm 5\Rightarrow \left[\begin{matrix} a=4\\ a=-6\end{matrix}\right.\)

Nếu $a=4$ \(\leftrightarrow x^2+3x=4\leftrightarrow x^2+3x-4=0\)

\(\leftrightarrow (x-1)(x+4)=0\Rightarrow x=1\) hoặc $x=-4$

Nếu \(a=-6\leftrightarrow x^2+3x=-6\leftrightarrow x^2+3x+6=0\leftrightarrow (x+\frac{3}{2})^2+\frac{15}{4}=0\)(vô lý)

Do đó pt có nghiệm $x=1$ hoặc $x=-4$

bạn tải ảnh về r up lại đi bạn

\(a,4\left(x-3\right)^2-\left(2x-1\right)^2\ge12\)

\(\Leftrightarrow4x^2-24x+36-4x^2-4x+1\ge12\)

\(\Leftrightarrow-28x+37\ge12\)

\(\Leftrightarrow-28x\ge12-37\)

\(\Leftrightarrow-28x\ge-25\)

\(\Leftrightarrow x\le\dfrac{25}{28}\)

Vậy \(S=\left\{x\left|x\le\dfrac{25}{28}\right|\right\}\)

b, \(\left(x-4\right)\left(x+4\right)\ge\left(x+3\right)^2+5\)

\(\Leftrightarrow x^2-16\ge x^2+6x+9+5\)

\(\Leftrightarrow x^2-x^2-6x\ge9+5+16\)

\(\Leftrightarrow-6x\ge30\)

\(\Leftrightarrow x\le-5\)

Vậy \(S=\left\{x\left|x\le-5\right|\right\}\)

\(c,\left(3x-1\right)^2-9\left(x+2\right)\left(x-2\right)< 5x\)

\(\Leftrightarrow9x^2-6x-1-9x^2+36< 5x\)

\(\Leftrightarrow9x^2-9x^2-6x-5x+36+1< 0\)

\(\Leftrightarrow-11x+37< 0\)

\(\Leftrightarrow-11x< -37\)

\(\Leftrightarrow x>\dfrac{37}{11}\)

vậy \(S=\left\{x\left|x>\dfrac{37}{11}\right|\right\}\)

a: =>2x-4+3+3y=-2 và 3x-6-2-2y=-3

=>2x+3y=-2+4-3=2-3=-1 và 3x-2y=-3+6+2=5

=>x=1; y=-1

b: =>x^2-x+xy-y=x^2+x-xy-y+2xy

=>-x-y=x-y và y^2+y-yx-x=y^2-2y+xy-2x-2xy

=>x=0 và y-x=-2y-2x

=>x=0 và y=0

`a,(x+3)(x^2+2021)=0`

`x^2+2021>=2021>0`

`=>x+3=0`

`=>x=-3`

`2,x(x-3)+3(x-3)=0`

`=>(x-3)(x+3)=0`

`=>x=+-3`

`b,x^2-9+(x+3)(3-2x)=0`

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

`=>(x+3)(-x)=0`

`=>` $\left[ \begin{array}{l}x=0\\x=-3\end{array} \right.$

`d,3x^2+3x=0`

`=>3x(x+1)=0`

`=>` $\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.$

`e,x^2-4x+4=4`

`=>x^2-4x=0`

`=>x(x-4)=0`

`=>` $\left[ \begin{array}{l}x=0\\x=4\end{array} \right.$

1) a) \(\left(x+3\right).\left(x^2+2021\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\x^2+2021=0\end{matrix}\right.\\\left[{}\begin{matrix}x=-3\left(nhận\right)\\x^2=-2021\left(loại\right)\end{matrix}\right. \)

=> S={-3}

Bài 1: 

a) Ta có: \(\left(x+3\right)\left(x^2+2021\right)=0\)

mà \(x^2+2021>0\forall x\)

nên x+3=0

hay x=-3

Vậy: S={-3}

Bài 2: 

b) Ta có: \(x\left(x-3\right)+3\left(x-3\right)=0\)

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

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

Vậy: S={3;-3}

a) (x² - 4x)² = 4(x² - 4x) 

<=> (x² - 4x)(x² - 4x - 4) = 0

<=> x(x - 4)(x² - 4x - 4) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\\left(x-2\right)^2=8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=\pm\sqrt{8}+2\end{matrix}\right.\)

b) (x + 2)² - x + 1 = (x - 1)(x + 1) 

<=> x² + 4x + 4 - x + 1 = x² - 1

<=> 3x + 5 = -1

<=> x = -2 

a) đặt \(\left(x^2+x\right)\)là \(y\)

ta có: \(3y^2-7y+4\)\(=0\)

<=>\(\left(3y-4\right)\left(y-1\right)=0\)

còn lại bạn tự xử nhé