2:

a: =>2x^2-4x-2=x^2-x-2

=>x^2-3x=0

=>x=0(loại) hoặc x=3

b: =>(x+1)(x+4)<0

=>-4<x<-1

d: =>x^2-2x-7=-x^2+6x-4

=>2x^2-8x-3=0

=>\(x=\dfrac{4\pm\sqrt{22}}{2}\)

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

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2-x+4\right)=0\)

\(\Leftrightarrow x=1\left(h\right)x=-2\left(h\right)x^2-x+4=0\)

Mà \(x^2-x+4=\left(x-\frac{1}{2}\right)^2+\frac{15}{4}>0\)

\(\Rightarrow x=1\left(h\right)x=-2\)

\(\dfrac{1}{x+2}+\dfrac{6x+12}{x^3+8}-\dfrac{7}{x^2-2x+4}=0\) \(\left(đk:x\ne-2\right)\)

\(\Leftrightarrow\dfrac{x^2-2x+4+6x+12-7\left(x+2\right)}{x^3+8}=0\)

\(\Leftrightarrow\dfrac{x^2-3x+2}{x^3+8}=0\)

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)(TM)

Vậy ...

dk : x khac -2 

\(\Rightarrow x^2-2x+4+6x+12-7\left(x+2\right)=0\)

\(\Leftrightarrow x^2+4x+16-7x-14=0\Leftrightarrow x^2-3x+2=0\)

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

Sory sor mình không giải cặn cẽ dc

X = 1

Nhớ k đúng

k đúng

còn có -2 nữa

a: Ta có: \(x^2+3x+4=0\)

\(\text{Δ}=3^2-4\cdot1\cdot4=9-16=-7< 0\)

Do đó: Phương trình vô nghiệm

1) \(x^4-6x^3-x^2+54x-72=0\)

\(\Leftrightarrow x^3\left(x-2\right)-4x^2\left(x-2\right)-9x\left(x-2\right)+36\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-4x^2-9x+36\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-4\right)-9\left(x-4\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-4\right)\left(x^2-9\right)=0\)

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

Tự làm nốt...

2) \(x^4-5x^2+4=0\)

\(\Leftrightarrow x^2\left(x^2-1\right)-4\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)=0\)

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

Tự làm nốt...

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

\(\Leftrightarrow x^3\left(x-2\right)-6x\left(x-2\right)-4\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-6x-4\right)=0\)

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

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

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left[\left(x-1\right)^2-\left(\sqrt{3}\right)^2\right]=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1-\sqrt{3}\right)\left(x-1+\sqrt{3}\right)=0\)

...

\(2x^4-13x^3+20x^2-3x-2=0\)

\(\Leftrightarrow2x^3\left(x-2\right)-9x^2\left(x-2\right)+2x\left(x-2\right)+\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(2x^3-9x^2+2x+1\right)=0\)

Bí

\(2x^3-9x^2+2x+1\)

\(=2x^3-x^2-8x^2+4x-2x+1\)

\(=x^2\left(2x-1\right)-4x\left(2x-1\right)-\left(2x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x-1\right)\)

\(=\left(2x-1\right)\left(x^2-4x+4-5\right)\)

\(=\left(2x-1\right)\left[\left(x-2\right)^2-5\right]\)

.......

(x^2)^2+(x^2+6x+3^2)-1=0

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

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

(x+3)^2 luôn lớn hơn 0

nên x^2-1=0 => x=1

      x^2+1=0 => x vô nghiệm

@dcv_new: thử tách theo cách x^4+x^2+6x-6-2 thử đi:)) chắc cũng ra á:)

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

\(\Leftrightarrow\left(x^3+x^2+2x+8\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2-x+4\right)\left(x+2\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2-x+4\ne0\right)\Leftrightarrow\orbr{\begin{cases}x=-2\\x=1\end{cases}}\)( chắc dân chuyên như cậu hiểu chỗ này á ) 

mình học trường làng bạn :)))) mà mình đang cần cách nào mới lạ hơn cách này 

cách này cũ rích rồi 

Đặt \(x^2-6x=t\)

Ta có: \(\frac{21}{t}-t+4=0\Leftrightarrow t^2-4t-21=0\\ \Rightarrow\left(t-7\right)\left(t+3\right)=0\\ \Leftrightarrow\orbr{\begin{cases}t=7\\t=-3\end{cases}}\)

\(t=7\Rightarrow x^2-6x-7=0\Rightarrow\orbr{\begin{cases}x=7\\x=-1\end{cases}}\)

\(t=3\Rightarrow x^2-6x-3=0\Rightarrow\orbr{\begin{cases}x=3-\sqrt{12}\\x=3+\sqrt{12}\end{cases}}\)