Sửa đề: 9x^2-1+(3x-1)(x+2)=0

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

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

=>(3x-1)(4x+3)=0

=>x=-3/4 hoặc x=1/3

a. Dat \(x^2=t\left(t\ge0\right)\)

Suy ra PT:\(\orbr{\begin{cases}t^2=-4t+1\left(1\right)\left(x< 0\right)\\t^2=4t+1\left(2\right)\left(x\ge0\right)\end{cases}}\)

(1)\(\Leftrightarrow t^2+4t-1=0\)

\(\Leftrightarrow\left(t+2\right)^2-5=0\)

\(\Leftrightarrow\left(t+2+\sqrt{5}\right)\left(t+2-\sqrt{5}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}t=-2-\sqrt{5}\left(l\right)\\t=\sqrt{5}-2\left(n\right)\end{cases}}\)

Nghiem cua PT(1) la \(t=\sqrt{5}-2\)

(2)\(\Leftrightarrow t^2-4t-1=0\)

\(\Leftrightarrow\left(t-2\right)^2-5=0\)

\(\Leftrightarrow\left(t-2+\sqrt{5}\right)\left(t-2-\sqrt{5}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}t=2-\sqrt{5}\left(l\right)\\t=2+\sqrt{5}\left(n\right)\end{cases}}\)

Nghiem cua PT(2) la \(t=2+\sqrt{5}\)

Suy ra:\(\orbr{\begin{cases}x=\sqrt{\sqrt{5}-2}\\x=\sqrt{\sqrt{5}+2}\end{cases}}\)

b.\(x^3-3x^2+9x-9=0\)

\(\Leftrightarrow\left(x-3\right)^3=-18\)

\(\Leftrightarrow x-3=-\sqrt[3]{18}\)

\(\Leftrightarrow x=3-\sqrt[3]{18}\)

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

\(\Rightarrow x^2\left(x-3\right)+9\left(x-3\right)+18=0\)

\(\Rightarrow\left(x^2+9\right)\left(x-3\right)=-18\)

từ đây bạn xét các TH nhá ! 

 Chú ý : Vì \(x^2+9\ge9\forall\) để xét ít Th hơn

a, x^4 - 4x - 1 = 0
<=> x^4 +2x^2 + 1 -2x^2 - 4x - 2 = 0 
<=> (x^2 + 1)^2 - 2(x + 1)^2 = 0 
<=> (x^2 + x*can(2) + 1 + can2))*(x^2 - x*can2) + 1 - can2)) = 0 
<=> x^2 + x*can(2) + 1 + can(2) = 0 (1) 
hoac x^2 - x*can(2) + 1 - can(2) = 0 (2) 
PT (1) vo nghiem 
PT (2) co 2 nghiem phan biet: 
x1 = (can2) + can(-2 + 4can(2)))/2 
x2 = (can(2) + can(-2 + 4can(2)))/2 

sorry b, phải là cái này nha

T sợ chỉ dám liên hợp thôi, nhường cách bình phương cho 1 ng` chăm chỉ :(

\(pt\Leftrightarrow6x+3x\sqrt{9x^2+3}+4x+2+\left(4x+2\right)\sqrt{x^2+x+1}=0\)

\(\Leftrightarrow2\left(5x+1\right)+\left(3x\sqrt{9x^2+3}+\dfrac{6\sqrt{21}}{25}\right)+\left(\left(4x+2\right)\sqrt{x^2+x+1}-\dfrac{6\sqrt{21}}{25}\right)=0\)

\(\Leftrightarrow2\left(5x+1\right)+\dfrac{\dfrac{27}{625}\left(5x-1\right)\left(5x+1\right)\left(75x^2+28\right)}{3x\sqrt{9x^2+3}-\dfrac{6\sqrt{21}}{25}}+\dfrac{\dfrac{4}{625}\left(5x+1\right)\left(5x+4\right)\left(100x^2+100x+109\right)}{\left(4x+2\right)\sqrt{x^2+x+1}+\dfrac{6\sqrt{21}}{25}}=0\)

\(\Leftrightarrow\left(5x+1\right)\left(2+\dfrac{\dfrac{27}{625}\left(5x-1\right)\left(75x^2+28\right)}{3x\sqrt{9x^2+3}-\dfrac{6\sqrt{21}}{25}}+\dfrac{\dfrac{4}{625}\left(5x+4\right)\left(100x^2+100x+109\right)}{\left(4x+2\right)\sqrt{x^2+x+1}+\dfrac{6\sqrt{21}}{25}}\right)=0\)

\(\Rightarrow5x+1=0\Rightarrow x=-\dfrac{1}{5}\)