\(\sqrt{81x^2}-8x=\sqrt{\left(9x\right)^2}-8x=\left|9x\right|-8x=9x-8x=x\) ( vì x > 0)

\(6.\sqrt{36x^2}-36x=6.\sqrt{\left(6x\right)^2}-36x=6.\left|6x\right|-36x=6.\left(-6x\right)-36x=-36x-36x=-72x\) (vì x < 0)

Bn có thể dùng CT toán hx đc ko??/ Mk ko hỉu cái đề!

\(\Leftrightarrow x^2+36x+324-334=0\)

\(\Leftrightarrow\left(x+18\right)^2=334\)

hay \(x\in\left\{\sqrt{334}-18;-\sqrt{334}-18\right\}\)

\(x^2+36x-10=0\\ \Leftrightarrow x\left(x+26\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-26\end{matrix}\right.\)

\(\Rightarrow\left(6x\right)^2-49=0\)

\(\Rightarrow\left(6x\right)^2=49-0=49=7^2\)

\(\Rightarrow6x=7\)

\(\Rightarrow x=\frac{7}{6}\)

Vậy: \(x=\frac{7}{6}\)

=>2x(x^2-11x+18)=0

=>x(x-2)(x-9)=0

=>\(x\in\left\{0;2;9\right\}\)

2x³ - 22x² + 36x = 0

2x(x² - 11x + 18) = 0

2x(x² - 2x - 9x + 18) = 0

2x[(x² - 2x) - (9x - 18)] = 0

2x[x(x - 2) - 9(x - 2)] = 0

2x(x - 2)(x - 9) = 0

2x = 0 hoặc x - 2 = 0 hoặc x - 9 = 0

*) 2x = 0

x = 0

*) x - 2 = 0

x = 2

*) x - 9 = 0

x = 9

Vậy x = 0; x = 2; x = 9

\(a,\Leftrightarrow\left(x+3\right)\left(x+3-2x-1\right)=0\\ \Leftrightarrow\left(x+3\right)\left(2-x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\\ b,\Leftrightarrow x\left(x^2-12x+36\right)=0\\ \Leftrightarrow x\left(x-6\right)^2=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\end{matrix}\right.\)

a, (x+3)² - ( 2x + 1 ).( x+3)=0              b,     x³-12x²+36x =0

=> (x+3).(x+3-2x-1)                             => x(x²-12x+36) = 0

=>(x+3).(-x+2)                                     => x(x-6)² = 0

=> x+3=0  <=> x=-3                            => x=0        <=> x=0

     -x+2=0 <=> x=-2                                 x-6= 0    <=> x=6

Đáp án C

Đề ko có vấn đề chứ ạ ? 

\(27x^2.x+69x^2+36x=0\)

Tương đương vs pt : \(\Leftrightarrow27x^3+69x^2+36x=0\)

\(\Leftrightarrow3x\left(9x^2+23x+12\right)=0\)

TH1 : \(3x=0\Leftrightarrow x=0\)

TH2 : \(\Delta=23^2-4.12.9=529-432=97>0\)

Phương trình có 2 nghiệm phân biệt

\(x_1=\frac{-23-\sqrt{97}}{3};x_2=\frac{-23+\sqrt{97}}{3}\)

a) (2x - 5)² - (5 + 2x) = 0

<=> 4x² - 22x + 20 = 0 

\(\Leftrightarrow\left(2x-\dfrac{11}{2}\right)^2=\dfrac{41}{4}\)

\(\Leftrightarrow x=\dfrac{\pm\sqrt{41}+11}{4}\)

b) \(27x^3-54x^2+36x=0\)

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

\(\Leftrightarrow x=0\) (Vì \(3x^2-6x+4=3\left(x-1\right)^2+1>0\forall x\))

c) x³ + 8 - (x + 2).(x - 4) = 0

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

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

\(\Leftrightarrow x=-2\) (Vì \(x^2-3x+8=\left(x-\dfrac{3}{2}\right)^2+\dfrac{23}{4}>0\))

d) \(x^6-1=0\)

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

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

\(\Leftrightarrow x^2-1=0\) (Vì \(x^4+x^2+1>0\))

\(\Leftrightarrow x=\pm1\)

\(d,x^6-1=0\\ \Leftrightarrow\left(x^2\right)^3-1^3=0\\ \Leftrightarrow\left(x^2-1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\\x^4+x^2+1=0\left(Vô.lí,vì:x^4\ge0;x^2\ge0,\forall x\in R\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\ c,\left(x^3+8\right)-\left(x+2\right)\left(x-4\right)=0\\ \Leftrightarrow\left(x^3+8\right)-\left(x^2-2x-8\right)=0\\ \Leftrightarrow x^3-x^2+2x+16=0\\ \Leftrightarrow x^3+2x^2-3x^2-6x+8x+16=0\\ \Leftrightarrow x^2\left(x+2\right)-3x\left(x+2\right)+8\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-3x+8\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2-3x+8=0\left(Vô.lí\right)\\x+2=0\end{matrix}\right.\Leftrightarrow x=-2\)

c)(x^3+ 8) - (x + 2)(x - 4) = 0
<=> x^3 -x^2 + 2x +8 + 8 = 0
<=> x^3 -x^2 + 2x + 16 = 0
<=> (x+2)(x^2-3x+8) = 0
=> x = -2